document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=518971>Question 518971</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 	1.	Which of the following statements regarding the coefficient of correlation is true? <BR>\n" );
document.write( "	A)	It ranges from –1.0 to +1.0 inclusive <BR>\n" );
document.write( "	B)	It measures the strength of the relationship between two variables <BR>\n" );
document.write( "	C)	A value of 0.00 indicates two variables are not related <BR>\n" );
document.write( "	D)	All of the above <BR>\n" );
document.write( "	E)	None of the above \r<BR>\n" );
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document.write( "	2.	What does a coefficient of correlation of 0.70 infer? <BR>\n" );
document.write( "	A)	Almost no correlation because 0.70 is close to 1.0 <BR>\n" );
document.write( "	B)	70% of the variation in one variable is explained by the other <BR>\n" );
document.write( "	C)	Coefficient of determination is 0.49 <BR>\n" );
document.write( "	D)	Coefficient of nondetermination is 0.30 <BR>\n" );
document.write( "	E)	None of the above \r<BR>\n" );
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document.write( "	3.	If the correlation coefficient between two variables equals zero, what can be said of the variables X and Y? <BR>\n" );
document.write( "	A)	Not related <BR>\n" );
document.write( "	B)	Dependent on each other <BR>\n" );
document.write( "	C)	Highly related <BR>\n" );
document.write( "	D)	All of the above are correct <BR>\n" );
document.write( "	E)	None of the above is correct \r<BR>\n" );
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document.write( "	4.	What can we conclude if the coefficient of determination is 0.94? <BR>\n" );
document.write( "	A)	Strength of relationship is 0.94 <BR>\n" );
document.write( "	B)	Direction of relationship is positive <BR>\n" );
document.write( "	C)	94% of total variation in one variable is explained by variation in the other variable <BR>\n" );
document.write( "	D)	All of the above are correct <BR>\n" );
document.write( "	E)	None of the above is correct \r<BR>\n" );
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document.write( "	5.	Which value of r indicates a stronger correlation than 0.40? <BR>\n" );
document.write( "	A)	–0.30 <BR>\n" );
document.write( "	B)	–0.50 <BR>\n" );
document.write( "	C)	+0.38 <BR>\n" );
document.write( "	D)	0 <BR>\n" );
document.write( "	E)	None of the above \r<BR>\n" );
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document.write( "	6.	In the regression equation, what does the letter “a” represent? <BR>\n" );
document.write( "	A)	Y intercept <BR>\n" );
document.write( "	B)	Slope of the line <BR>\n" );
document.write( "	C)	Any value of the independent variable that is selected <BR>\n" );
document.write( "	D)	None of the above \r<BR>\n" );
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document.write( "	7.	In the regression equation, what does the letter “b” represent? <BR>\n" );
document.write( "	A)	Y intercept <BR>\n" );
document.write( "	B)	Slope of the line <BR>\n" );
document.write( "	C)	Any value of the independent variable that is selected <BR>\n" );
document.write( "	D)	Value of Y when X=0 <BR>\n" );
document.write( "	E)	None of the above \r<BR>\n" );
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document.write( "	8.	Suppose the least squares regression equation is Y' = 1202 + 1,133X. When X = 3, what does Y' equal? <BR>\n" );
document.write( "	A)	5,734 <BR>\n" );
document.write( "	B)	8,000 <BR>\n" );
document.write( "	C)	4,601 <BR>\n" );
document.write( "	D)	4,050 <BR>\n" );
document.write( "	E)	None of the above \r<BR>\n" );
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document.write( "	9.	What is the general form of the regression equation? <BR>\n" );
document.write( "	A)	Y' = ab <BR>\n" );
document.write( "	B)	Y' = a + bX <BR>\n" );
document.write( "	C)	Y' = a – bX <BR>\n" );
document.write( "	D)	Y' = abX <BR>\n" );
document.write( "	E)	None of the above \r<BR>\n" );
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document.write( "	10.	Which of the following are true assumptions underlying linear regression: 1)  for each value of X, there is a group of Y values which are normally distributed; 2)  the means of these normal distributions of Y values all lie on the straight line of regression; and/or 3)  the standard deviations of these normal distributions are equal? <BR>\n" );
document.write( "	A)	Only (1) and (2) <BR>\n" );
document.write( "	B)	Only (1) and (3) <BR>\n" );
document.write( "	C)	Only (2) and (3) <BR>\n" );
document.write( "	D)	All of them <BR>\n" );
document.write( "	E)	None of them \r<BR>\n" );
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document.write( "	11.	Based on the regression equation, we can <BR>\n" );
document.write( "	A)	predict the value of the dependent variable given a value of  the independent variable. <BR>\n" );
document.write( "	B)	predict the value of the independent variable given a value of the dependent variable. <BR>\n" );
document.write( "	C)	measure the association between two variables. <BR>\n" );
document.write( "	D)	all of the above. <BR>\n" );
document.write( "	E)	none of the above. \r<BR>\n" );
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document.write( "	12.	What is the chart called when the paired data (the dependent and independent variables) are plotted? <BR>\n" );
document.write( "	A)	Scatter diagram <BR>\n" );
document.write( "	B)	Bar <BR>\n" );
document.write( "	C)	Pie <BR>\n" );
document.write( "	D)	Linear regression <BR>\n" );
document.write( "	E)	None of the above \r<BR>\n" );
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document.write( "	13.	In the equation Y' = a + bX, what is Y'? <BR>\n" );
document.write( "	A)	Slope of the line <BR>\n" );
document.write( "	B)	Y intercept <BR>\n" );
document.write( "	C)	Predicted value of Y, given a specific X value <BR>\n" );
document.write( "	D)	Value of Y when X=0 <BR>\n" );
document.write( "	E)	None of the above \r<BR>\n" );
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document.write( "14.	Assume the least squares equation is Y' = 10 + 20X.  What does the value of 10 in the equation indicate? <BR>\n" );
document.write( "	A)	Y intercept <BR>\n" );
document.write( "	B)	For each unit increased in Y, X increases by 10 <BR>\n" );
document.write( "	C)	For each unit increased in X, Y increases by 10 <BR>\n" );
document.write( "	D)	None of the above \r<BR>\n" );
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document.write( "	15.	In the least squares equation, Y' = 10 + 20X the value of 20 indicates <BR>\n" );
document.write( "	A)	the Y intercept. <BR>\n" );
document.write( "	B)	each unit increased in X, Y increases by 20. <BR>\n" );
document.write( "	C)	each unit increased in Y, X increases by 20. <BR>\n" );
document.write( "	D)	none of the above. \r<BR>\n" );
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document.write( "	16.	If the regression equation is Y' = 2 – 0.4X, what is the value of Y' when <BR>\n" );
document.write( "		X = –3? <BR>\n" );
document.write( "	A)	0.8 <BR>\n" );
document.write( "	B)	3.2 <BR>\n" );
document.write( "	C)	–10.0 <BR>\n" );
document.write( "	D)	14.0 <BR>\n" );
document.write( "	E)	None of the above \r<BR>\n" );
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document.write( "Use the following to answer questions 17-18:\r<BR>\n" );
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document.write( "A sales manager for an advertising agency believes there is a relationship between the number of contacts and the amount of the sales.  To verify this belief, the following data was collected:\r<BR>\n" );
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document.write( "17.	What is the dependent variable? <BR>\n" );
document.write( "	A)	Salesperson <BR>\n" );
document.write( "	B)	Number of contacts <BR>\n" );
document.write( "	C)	Amount of sales <BR>\n" );
document.write( "	D)	All the above <BR>\n" );
document.write( "	E)	None of the above \r<BR>\n" );
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document.write( "	18.	What is the independent variable? <BR>\n" );
document.write( "	A)	Salesperson <BR>\n" );
document.write( "	B)	Number of contacts <BR>\n" );
document.write( "	C)	Amount of sales <BR>\n" );
document.write( "	D)	All the above <BR>\n" );
document.write( "	E)	None of the above \r<BR>\n" );
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document.write( "Use the following to answer question 19:\r<BR>\n" );
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document.write( "A regression analysis yields the following information:<BR>\n" );
document.write( "Y' = 2.24 + 1.49 X\r<BR>\n" );
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document.write( "	19.	Estimate the value of Y' when X = 4. <BR>\n" );
document.write( "	A)	10.45 <BR>\n" );
document.write( "	B)	3.73 <BR>\n" );
document.write( "	C)	8.20 <BR>\n" );
document.write( "	D)	Cannot be computed \r<BR>\n" );
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document.write( "	20.	If the coefficient of multiple determination is 0.81, what percent of variation is not explained? <BR>\n" );
document.write( "	A)	19% <BR>\n" );
document.write( "	B)	90% <BR>\n" );
document.write( "	C)	66% <BR>\n" );
document.write( "	D)	81% <BR>\n" );
document.write( "	E)	None of the above \r<BR>\n" );
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document.write( "	21.	When does multicollinearity occur in a multiple regression analysis? <BR>\n" );
document.write( "	A)	Dependent variables are highly correlated <BR>\n" );
document.write( "	B)	Independent variables are minimally correlated <BR>\n" );
document.write( "	C)	Independent variables are highly correlated <BR>\n" );
document.write( "	D)	Independent variables have no correlation <BR>\n" );
document.write( "	E)	None of the above \r<BR>\n" );
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document.write( "	22.	How is the Y intercept in the multiple regression equation represented? <BR>\n" );
document.write( "	A)	b1 <BR>\n" );
document.write( "	B)	x1 <BR>\n" );
document.write( "	C)	b2 <BR>\n" );
document.write( "	D)	x2 <BR>\n" );
document.write( "	E)	None of the above \r<BR>\n" );
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document.write( "	23.	In multiple regression, a dummy variable can be included in a multiple regression model as <BR>\n" );
document.write( "	A)	An additional quantitative variable <BR>\n" );
document.write( "	B)	A nominal variable with three or more values <BR>\n" );
document.write( "	C)	A nominal variable with only two values <BR>\n" );
document.write( "	D)	A new regression coefficient \r<BR>\n" );
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document.write( "	24.	Multiple regression analysis is applied when analyzing the relationship between <BR>\n" );
document.write( "	A)	An independent variable and several dependent variables <BR>\n" );
document.write( "	B)	A dependent variable and several independent variables <BR>\n" );
document.write( "	C)	Several dependent variables and several independent variables <BR>\n" );
document.write( "	D)	Several regression equations and a single sample <BR>\n" );
document.write( "	E)	None of the above \r<BR>\n" );
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document.write( "Use the following to answer questions 25-28:\r<BR>\n" );
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document.write( "The following correlations were computed as part of a multiple regression analysis that used education, job, and age to predict income.\r<BR>\n" );
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document.write( "	25.	What is this table called? <BR>\n" );
document.write( "	A)	Net regression coefficients <BR>\n" );
document.write( "	B)	Coefficients of nondetermination <BR>\n" );
document.write( "	C)	Analysis of variance <BR>\n" );
document.write( "	D)	Correlation matrix <BR>\n" );
document.write( "	E)	None of the above \r<BR>\n" );
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document.write( "	26.	Which is the dependent variable? <BR>\n" );
document.write( "	A)	Income <BR>\n" );
document.write( "	B)	Age <BR>\n" );
document.write( "	C)	Education <BR>\n" );
document.write( "	D)	Job <BR>\n" );
document.write( "	E)	None of the above \r<BR>\n" );
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document.write( "	27.	Which independent variable has the strongest association with the dependent variable? <BR>\n" );
document.write( "	A)	Income <BR>\n" );
document.write( "	B)	Age <BR>\n" );
document.write( "	C)	Education <BR>\n" );
document.write( "	D)	Job <BR>\n" );
document.write( "	E)	None of the above \r<BR>\n" );
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document.write( "	28.	Which independent variable has the weakest association with the dependent variable? <BR>\n" );
document.write( "	A)	Income <BR>\n" );
document.write( "	B)	Age <BR>\n" );
document.write( "	C)	Education <BR>\n" );
document.write( "	D)	Job <BR>\n" );
document.write( "	E)	None of the above \r<BR>\n" );
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document.write( "Use the following to answer question 29:\r<BR>\n" );
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document.write( "Twenty-one executives in a large corporation were randomly selected for a study in which several factors were examined to determine their effect on annual salary (expressed in $000's).  The factors selected were age, seniority, years of college, number of company divisions they had been exposed to and the level of their responsibility.  A regression analysis was performed using a popular spreadsheet program with the following regression output:\r<BR>\n" );
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document.write( "	29.	Which one of the following is the dependent variable? <BR>\n" );
document.write( "	A)	Age <BR>\n" );
document.write( "	B)	Seniority <BR>\n" );
document.write( "	C)	Level of responsibility <BR>\n" );
document.write( "	D)	Annual salary <BR>\n" );
document.write( "	E)	Experience in number of company divisions \r<BR>\n" );
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document.write( "Use the following to answer questions 30-31:\r<BR>\n" );
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document.write( "A manager at a local bank analyzed the relationship between monthly salary and three independent variables: length of service (measured in months), gender ( 0 = female, 1 = male) and job type (0 = clerical, 1 = technical).  The following ANOVA summarizes the regression results:\r<BR>\n" );
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document.write( "	30.	In the regression model, which of the following are considered dummy variables? <BR>\n" );
document.write( "	A)	Intercept <BR>\n" );
document.write( "	B)	Service <BR>\n" );
document.write( "	C)	Service and gender <BR>\n" );
document.write( "	D)	Gender and job <BR>\n" );
document.write( "	E)	Service, gender, and job \r<BR>\n" );
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document.write( "	31.	The results for the variable gender show that <BR>\n" );
document.write( "	A)	males average $222.78 more than females in monthly salary <BR>\n" );
document.write( "	B)	females average $222.78 more than males in monthly salary <BR>\n" );
document.write( "	C)	gender is not related to monthly salary <BR>\n" );
document.write( "	D)	Gender and months of service are correlated. \r<BR>\n" );
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document.write( "Family	Food	Income	Size	Region		Variable	Description<BR>\n" );
document.write( "1	5.04	73.98	4	2			<BR>\n" );
document.write( "2	4.08	54.9	2	2		Family	Identification Number<BR>\n" );
document.write( "3	5.76	94.14	4	1		Food	Dollars (000) Spent Per Year<BR>\n" );
document.write( "4	3.48	52.02	1	3		Income	Gross Pay ($000) Per Year<BR>\n" );
document.write( "5	4.2	65.7	2	3		Size	Family Size<BR>\n" );
document.write( "6	4.8	53.64	4	1		Region	Area of the Country<BR>\n" );
document.write( "7	4.32	79.64	3	2			<BR>\n" );
document.write( "8	5.04	68.58	4	3			<BR>\n" );
document.write( "9	6.12	165.6	5	2			<BR>\n" );
document.write( "10	3.24	64.8	1	1			<BR>\n" );
document.write( "11	4.8	138.42	3	1			<BR>\n" );
document.write( "12	3.24	125.82	1	2			<BR>\n" );
document.write( "13	6.6	77.58	7	2			<BR>\n" );
document.write( "14	4.92	171.36	2	1			<BR>\n" );
document.write( "15	6.6	82.08	9	4			<BR>\n" );
document.write( "16	5.4	141.3	3	3			<BR>\n" );
document.write( "17	6	36.9	5	2			<BR>\n" );
document.write( "18	5.4	56.88	4	1			<BR>\n" );
document.write( "19	3.36	71.82	1	2			<BR>\n" );
document.write( "20	4.68	69.48	3	4			<BR>\n" );
document.write( "21	4.32	54.36	2	3			<BR>\n" );
document.write( "22	5.52	87.66	5	4			<BR>\n" );
document.write( "23	4.56	38.16	3	2			<BR>\n" );
document.write( "24	5.4	43.74	7	1			<BR>\n" );
document.write( "25	4.8	48.42	5	4			<BR>\n" );
document.write( "							<BR>\n" );
document.write( "							<BR>\n" );
document.write( "Results of multiple regression for Food: All Variables		<BR>\n" );
document.write( "							<BR>\n" );
document.write( "Summary measures					<BR>\n" );
document.write( "	Multiple R	0.9103					<BR>\n" );
document.write( "	R-Square	0.8287					<BR>\n" );
document.write( "	Adj R-Square	0.7945					<BR>\n" );
document.write( "	StErr of Est	0.4369					<BR>\n" );
document.write( "							<BR>\n" );
document.write( "ANOVA Table						<BR>\n" );
document.write( "	Source	df	SS	MS	F	p-value	<BR>\n" );
document.write( "	Explained	4	18.4753	4.6188	24.1935	0.0000	<BR>\n" );
document.write( "	Unexplained	20	3.8182	0.1909			<BR>\n" );
document.write( "							<BR>\n" );
document.write( "Regression coefficients					<BR>\n" );
document.write( "		Coefficient	Std Err	t-value	p-value		<BR>\n" );
document.write( "	Constant	2.9707	0.3516	8.4479	0.0000		<BR>\n" );
document.write( "	Family	-0.0051	0.0131	-0.3896	0.7010		<BR>\n" );
document.write( "	Income	0.0059	0.0024	2.4723	0.0225		<BR>\n" );
document.write( "	Size	0.4318	0.0456	9.4738	0.0000		<BR>\n" );
document.write( "	Region	-0.0296	0.0897	-0.3300	0.7448		\r<BR>\n" );
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document.write( "32.	Write the regression equation for the model presented in the preceding table {Results of multiple regression for Food: All Variables } on page 8.\r<BR>\n" );
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document.write( "33.	If the Family identification number is 20, the Income is 80, the family Size is 2, and the Region is 4: what is the projected Food expenditure?\r<BR>\n" );
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document.write( "34.	What percent of the variation can be explained in the model developed on page 8?\r<BR>\n" );
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document.write( "35.	List any variable(s) that should be removed {or altered} from the equation?<BR>\n" );
document.write( "Family	Food	Income	Size	Region	Region_1	Region_2	Region_3	Region_4<BR>\n" );
document.write( "1	5.04	73.98	4	2	0	1	0	0<BR>\n" );
document.write( "2	4.08	54.9	2	2	0	1	0	0<BR>\n" );
document.write( "3	5.76	94.14	4	1	1	0	0	0<BR>\n" );
document.write( "4	3.48	52.02	1	3	0	0	1	0<BR>\n" );
document.write( "5	4.2	65.7	2	3	0	0	1	0<BR>\n" );
document.write( "6	4.8	53.64	4	1	1	0	0	0<BR>\n" );
document.write( "7	4.32	79.64	3	2	0	1	0	0<BR>\n" );
document.write( "8	5.04	68.58	4	3	0	0	1	0<BR>\n" );
document.write( "9	6.12	165.6	5	2	0	1	0	0<BR>\n" );
document.write( "10	3.24	64.8	1	1	1	0	0	0<BR>\n" );
document.write( "11	4.8	138.42	3	1	1	0	0	0<BR>\n" );
document.write( "12	3.24	125.82	1	2	0	1	0	0<BR>\n" );
document.write( "13	6.6	77.58	7	2	0	1	0	0<BR>\n" );
document.write( "14	4.92	171.36	2	1	1	0	0	0<BR>\n" );
document.write( "15	6.6	82.08	9	4	0	0	0	1<BR>\n" );
document.write( "16	5.4	141.3	3	3	0	0	1	0<BR>\n" );
document.write( "17	6	36.9	5	2	0	1	0	0<BR>\n" );
document.write( "18	5.4	56.88	4	1	1	0	0	0<BR>\n" );
document.write( "19	3.36	71.82	1	2	0	1	0	0<BR>\n" );
document.write( "20	4.68	69.48	3	4	0	0	0	1<BR>\n" );
document.write( "21	4.32	54.36	2	3	0	0	1	0<BR>\n" );
document.write( "22	5.52	87.66	5	4	0	0	0	1<BR>\n" );
document.write( "23	4.56	38.16	3	2	0	1	0	0<BR>\n" );
document.write( "24	5.4	43.74	7	1	1	0	0	0<BR>\n" );
document.write( "25	4.8	48.42	5	4	0	0	0	1<BR>\n" );
document.write( "								<BR>\n" );
document.write( "								<BR>\n" );
document.write( "Variable	Description							<BR>\n" );
document.write( "Family	Identification Number							<BR>\n" );
document.write( "Food	Dollars (000) Spent Per Year							<BR>\n" );
document.write( "Income	Gross Pay ($000) Per Year							<BR>\n" );
document.write( "Size	Family Size							<BR>\n" );
document.write( "Region	Area of the Country							<BR>\n" );
document.write( "								<BR>\n" );
document.write( "Results of multiple regression for Food							<BR>\n" );
document.write( "								<BR>\n" );
document.write( "Summary measures							<BR>\n" );
document.write( "	Multiple R	0.9187						<BR>\n" );
document.write( "	R-Square	0.8441						<BR>\n" );
document.write( "	Adj R-Square	0.8031						<BR>\n" );
document.write( "	StErr of Est	0.4277						<BR>\n" );
document.write( "								<BR>\n" );
document.write( "ANOVA Table							<BR>\n" );
document.write( "	Source	df	SS	MS	F	p-value		<BR>\n" );
document.write( "	Explained	5	18.8177	3.7635	20.5732	0.0000		<BR>\n" );
document.write( "	Unexplained	19	3.4758	0.1829				<BR>\n" );
document.write( "								<BR>\n" );
document.write( "Regression coefficients							<BR>\n" );
document.write( "		Coefficient	Std Err	t-value	p-value			<BR>\n" );
document.write( "	Constant	2.7183	0.3239	8.3922	0.0000			<BR>\n" );
document.write( "	Income	0.0061	0.0023	2.6525	0.0157			<BR>\n" );
document.write( "	Size	0.4585	0.0486	9.4407	0.0000			<BR>\n" );
document.write( "	Region_2	0.0210	0.2166	0.0970	0.9238			<BR>\n" );
document.write( "	Region_3	0.1997	0.2590	0.7711	0.4502			<BR>\n" );
document.write( "	Region_4	-0.2821	0.2856	-0.9877	0.3357			<BR>\n" );
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document.write( "Referring to the preceding table { Results of multiple regression for Food } on page 10:\r<BR>\n" );
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document.write( "36.	What is the predicted Food expenditure for a family Size of 2, with an Income of 80, living in <BR>\n" );
document.write( "Region 1?\r<BR>\n" );
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document.write( "37.What is the predicted Food expenditure for a family Size of 2, with an Income of 80, living in <BR>\n" );
document.write( "Region 4?\r<BR>\n" );
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document.write( "38.	List any variable(s) that should be removed {or altered} from the equation?\r<BR>\n" );
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document.write( "39.	Which regression model is best?  The model presented on page 8 or the model presented on page 10?\r<BR>\n" );
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document.write( "40.	Explain why you chose the “best” model.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #345314 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=345314\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your length list of problems is clogging up the posted list.<BR>\n" );
document.write( "Please submit your questions a few at a time.<BR>\n" );
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document.write( "1. Which of the following statements regarding the coefficient of correlation is true? <BR>\n" );
document.write( "A) It ranges from –1.0 to +1.0 inclusive <BR>\n" );
document.write( "B) It measures the strength of the relationship between two variables <BR>\n" );
document.write( "C) A value of 0.00 indicates two variables are not related <BR>\n" );
document.write( "D) All of the above <BR>\n" );
document.write( "E) None of the above<BR>\n" );
document.write( "Ans: D<BR>\n" );
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document.write( "2. What does a coefficient of correlation of 0.70 infer? <BR>\n" );
document.write( "A) Almost no correlation because 0.70 is close to 1.0 <BR>\n" );
document.write( "B) 70% of the variation in one variable is explained by the other <BR>\n" );
document.write( "C) Coefficient of determination is 0.49 <BR>\n" );
document.write( "D) Coefficient of nondetermination is 0.30 <BR>\n" );
document.write( "E) None of the above<BR>\n" );
document.write( "Ans: E<BR>\n" );
document.write( "============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "============ \r<BR>\n" );
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document.write( " </SPAN>\n" );
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