Regression
1)
Consider the following sample data for the relationship between advertising budget and sales for Product A:
Observation  1  2  3  4  5  6  7  8  9  10 

Advertising ($)  30,000  30,000  40,000  50,000  50,000  50,000  60,000  70,000  80,000  80,000 
Sales ($)  179,000  183,000  253,000  308,000  301,000  308,000  376,000  418,000  486,000  499,000 
What is the slope of the "leastsquares" bestfit regression line?
Please round your answer to the nearest hundredth.
2)
Consider the following sample data for the relationship between advertising budget and sales for Product A:
Observation  1  2  3  4  5  6  7  8  9  10 

Advertising ($)  70,000  80,000  80,000  90,000  100,000  100,000  110,000  110,000  120,000  130,000 
Sales ($)  432,000  478,000  484,000  552,000  605,000  594,000  688,000  674,000  713,000  784,000 
What is the predicted sales quantity for an advertising budget of $95,000?
Please round your answer to the nearest integer.
Note that the correct answer will be evaluated based on the fullprecision result you would obtain using Excel.
3)
Consider the following sample data for the relationship between advertising budget and sales for Product A:
Observation  1  2  3  4  5  6  7  8  9  10 

Advertising ($)  40,000  50,000  50,000  60,000  70,000  70,000  80,000  80,000  90,000  100,000 
Sales ($)  239,000  315,000  311,000  363,000  432,000  438,000  493,000  486,000  535,000  603,000 
What is the R2 coefficient of determination value for the relationship between advertising and sales?
Please round your answer to the nearest hundredth.
Note that the correct answer will be evaluated based on the fullprecision result you would obtain using Excel.
Solution:
Question 1
Here, we have to construct the regression equation for the prediction of the dependent variable sales based on the independent variable advertising. The required regression output by using excel is given as below:
Regression Statistics 

Multiple R 
0.998240407 

R Square 
0.996483911 

Adjusted R Square 
0.9960444 

Standard Error 
7106.103751 

Observations 
10 

ANOVA 

df 
SS 
MS 
F 
Significance F 

Regression 
1 
1.14489E+11 
1.14489E+11 
2267.255136 
4.18513E11 

Residual 
8 
403973684.2 
50496710.53 

Total 
9 
1.14893E+11 

Coefficients 
Standard Error 
t Stat 
Pvalue 
Lower 95% 
Upper 95% 

Intercept 
289.4736842 
7313.456593 
0.039580967 
0.969397147 
17154.33482 
16575.38745 
Advertising ($) 
6.136842105 
0.128882738 
47.61570263 
4.18513E11 
5.83963798 
6.434046231 
What is the slope of the "leastsquares" bestfit regression line?
The slope of the least squares best fit regression line is given as 6.14.
There is an increment of $6.14 in the sales as per one dollar spend on advertising.
Question 2
Here, we have to construct the regression equation for the prediction of the dependent variable sales based on the independent variable advertising. The required regression output by using excel is given as below:
Regression Statistics 

Multiple R 
0.995766798 

R Square 
0.991551515 

Adjusted R Square 
0.990495455 

Standard Error 
11199.59156 

Observations 
10 

ANOVA 

df 
SS 
MS 
F 
Significance F 

Regression 
1 
1.17769E+11 
1.17769E+11 
938.9153641 
1.3978E09 

Residual 
8 
1003446809 
125430851.1 

Total 
9 
1.18772E+11 

Coefficients 
Standard Error 
t Stat 
Pvalue 
Lower 95% 
Upper 95% 

Intercept 
8085.106383 
19652.09968 
0.411411835 
0.691571555 
37232.7167 
53402.92946 
Advertising ($) 
5.982978723 
0.195255931 
30.64172587 
1.3978E09 
5.532717739 
6.433239708 
What is the predicted sales quantity for an advertising budget of $95,000?
The required regression equation is given as below:
Sales = 8085.106383 + 5.982978723*Advertising
We are given advertising = 95000
Sales = 8085.106383 + 5.982978723*95000
Sales = 576468.0851
Predicted sale = $576,468
Question 3
Here, we have to construct the regression equation for the prediction of the dependent variable sales based on the independent variable advertising. The required regression output by using excel is given as below:
Regression Statistics 

Multiple R 
0.997928258 

R Square 
0.995860807 

Adjusted R Square 
0.995343408 

Standard Error 
7739.145747 

Observations 
10 

ANOVA 

df 
SS 
MS 
F 
Significance F 

Regression 
1 
1.15281E+11 
1.15281E+11 
1924.74404 
8.03972E11 

Residual 
8 
479155015.2 
59894376.9 

Total 
9 
1.15761E+11 

Coefficients 
Standard Error 
t Stat 
Pvalue 
Lower 95% 
Upper 95% 

Intercept 
13057.75076 
9626.179767 
1.356483161 
0.211983555 
9140.259571 
35255.76109 
Advertising ($) 
5.919452888 
0.134925823 
43.87190491 
8.03972E11 
5.608313381 
6.230592394 
What is the R2 coefficient of determination value for the relationship between advertising and sales?
The Rsquare value or the coefficient of determination for the relationship between advertising and sales is given as 0.9959 or 99.59%. This means about 99.59% of the variation in the dependent variable sales is explained by the independent variable advertising.
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