SOLUTION: please help me to solve this prob, thank u.
where the owner of Haverty's Furniture Company was studying the relationship between sales and the amount spent on advertising. The sal
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-> SOLUTION: please help me to solve this prob, thank u.
where the owner of Haverty's Furniture Company was studying the relationship between sales and the amount spent on advertising. The sal
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Question 1131770: please help me to solve this prob, thank u.
where the owner of Haverty's Furniture Company was studying the relationship between sales and the amount spent on advertising. The sales information for the last four months is repeated below.
month Advertising expense ($ million) Sales revenue ($ million)
july 2 7
August 1 3
Sept 3 8
Oct 4 10
a) determine the regression of equation
b) interpret the values of a and b
c) estimate sales when $3 million is spent on advertising. Found 2 solutions by rothauserc, MathLover1:Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! There are 4 data points (2,7); (1,3); (3,8); (4,10)
:
The mean of the x values is (2+1+3+4)/4 = 2.5
:
The mean of the y values is (7+3+8+10)/4 = 7
:
The standard deviation of the x values is square root(((2-2.5)^2 +(1-2.5)^2 +(3-2.5)^2 +(4-2.5)^2)/(4-1)) = 1.29
:
The standard deviation of the y values is 2.94
:
The correlation factor(r) is ((1/(4-1)) ((2-2.5)*(7-7) +(1-2.5)*(3-7) +(3-2.5)*(8-7) +(4-2.5)*(10-7))/(1.29*2.94)) = 0.9668
:
slope(b) of the regression line = 0.9668 * 2.94 / 1.29 = 2.2034
:
a = 7 -2.2034 * 2.5 = 1.4915
:
a) Y = 2.2034X +1.4915
:
b) Y = bX +a, b = 2.2034 and a = 1.4915
:
Note a is the y intercept of the regression line and b is its slope
:
c) y = 2.2034 * 3 + 1.4915 = 8.1017
:
When $3 million is spent on advertising, the estimated sales is $8.1017 million
:
You can put this solution on YOUR website! month |Advertising expense ($ million) }|Sales revenue ($ million)
july |......................................................|............
August| ...................... ...........................|............
Sept|............................ ..........................| ..............
Oct|............................. ..........................|.............
Sum of
Sum of
Mean
Mean
a) determine the regression of equation
| || |....... |..... | |....... |..... | |....... |..... | |....... |..... |
Sum of squares
Sum of products
Regression Equation = ŷ =
b) interpret the values of and
ŷ =
For your data, the regression equation for Y is:
ŷ =
c) estimate sales when $ million is spent on advertising.
ŷ =
ŷ = million
