Question

# Regression 1) Consider the following sample data for the relationship between advertising budget and sales for...

Regression

1)

Consider the following sample data for the relationship between advertising budget and sales for Product A:

 Observation Advertising (\$) Sales (\$) 1 2 3 4 5 6 7 8 9 10 30,000 30,000 40,000 50,000 50,000 50,000 60,000 70,000 80,000 80,000 179,000 183,000 253,000 308,000 301,000 308,000 376,000 418,000 486,000 499,000

What is the slope of the "least-squares" best-fit regression line?

2)

Consider the following sample data for the relationship between advertising budget and sales for Product A:

 Observation Advertising (\$) Sales (\$) 1 2 3 4 5 6 7 8 9 10 70,000 80,000 80,000 90,000 100,000 100,000 110,000 110,000 120,000 130,000 432,000 478,000 484,000 552,000 605,000 594,000 688,000 674,000 713,000 784,000

What is the predicted sales quantity for an advertising budget of \$95,000?

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 Advertising (\$) Sales (\$) 1 2 3 4 5 6 7 8 9 10 40,000 50,000 50,000 60,000 70,000 70,000 80,000 80,000 90,000 100,000 239,000 315,000 311,000 363,000 432,000 438,000 493,000 486,000 535,000 603,000

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

Note that the correct answer will be evaluated based on the full-precision 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 4.18513E-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:

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.

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