Question

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 "least-squares" best-fit 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 full-precision 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 full-precision result you would obtain using Excel.

Answer 1

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	4.18513E-11
Residual	8	403973684.2	50496710.53
Total	9	1.14893E+11
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-289.4736842	7313.456593	-0.039580967	0.969397147	-17154.33482	16575.38745
Advertising ($)	6.136842105	0.128882738	47.61570263	4.18513E-11	5.83963798	6.434046231

What is the slope of the "least-squares" best-fit 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	1.3978E-09
Residual	8	1003446809	125430851.1
Total	9	1.18772E+11
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	8085.106383	19652.09968	0.411411835	0.691571555	-37232.7167	53402.92946
Advertising ($)	5.982978723	0.195255931	30.64172587	1.3978E-09	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	8.03972E-11
Residual	8	479155015.2	59894376.9
Total	9	1.15761E+11
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	13057.75076	9626.179767	1.356483161	0.211983555	-9140.259571	35255.76109
Advertising ($)	5.919452888	0.134925823	43.87190491	8.03972E-11	5.608313381	6.230592394

What is the R2 coefficient of determination value for the relationship between advertising and sales?

The R-square 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.