SOLUTION: Mr. James McWhinney, president of Daniel-James Financial Services, believes there is a relationship between the number of client contacts and the dollar amount of sales. To documen

Question 1206834: Mr. James McWhinney, president of Daniel-James Financial Services, believes there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, Mr. McWhinney gathered the following sample information. The x column indicates the number of client contacts last month, and the y column shows the value of sales ($ thousands) last month for each client sampled.

Number of
Contacts,
x Sales
($ thousands),
y Number of
Contacts,
x Sales
($ thousands),
y
37 $61 22 $33
41 76 18 22
19 34 38 48
29 47 22 32
49 95 17 31

a. Not available in Connect.

b. Determine the regression equation. (Do not round intermediate calculations and round the final answers to 4 decimal places. Negative answers should be indicated by a minus sign.)

b =
a =
y' =
+
x

c. Determine the estimated sales if 53 contacts are made. (Use the part b rounded answers to calculate the answer. Round the final answer to 3 decimal places.)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i used the regression calculator at https://www.statskingdom.com/linear-regression-calculator.html to solve this.

here are the the key results from using this calculator.

the regression equation is y = -8.5729 + 1.934 *
-8.5729 is the y-intercept
1.934 is the slope.

r = .9468 = correlation coefficient
it indicates a very strong correlation in a positive direction.

r^2 = .8965 = coefficient of determination
it indicates that almost 90% of the correlati0on is caused by the relationship between the variables.

the null hypothesis of the regression test states that there is no correlation, while the alternative states that there is a correlation.

the F-value of 69 and the p-value of .00003281 both support the conclusion that the null hypothesis is rejected in favor of the alternate hypothesis, indicating that a strong correlation exists.

i believe the critical f-value was around 5.32 as seen on the graph, and that the critical p-value for the test was .05.

the if the test f-value is greater than the critical f-value, the test is considered significant.
likewise, of the test p-value is less than the critical p-value, the test is also considered significant.
if significant, the null hypothesis is discarded in favor of the alternate hypothesis, as is the case in this test.

if 53 contacts are made, the regression equation becomes y = -8.5729 + 1.934 * 53.
that makes y = 93.9291 thousand.

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