The following data represent a company's yearly sales volume and its advertising expenditure over a period of...

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The following data represent acompany's yearly sales volume and its advertising expenditure overa period of 8 years.

            

Sales (Millions)

Advertising ($10,000)

15

32

16

33

18

35

17

34

16

36

19

37

19

39

24

42

To make sure the Excel regression package isinstalled.

Click “Tools”,à“Add-Ins”àchoose “Analysis Toolpak” and click“OK”.

To use the Excel regressionpackage,                                                     

Click “Tools”, à“DataAnalysis” and click “Regression”.

                                                            

            a.   Usethe method of least squares to compute an estimated regression linebetween sales and advertising.

            b.   Ifthe company's advertising expenditure is $400,000, what are thepredicted sales? Give the answer in dollars.

            c.   Whatdoes the slope of the estimated regression line indicate?

            d.   Whatis the coefficient of determination and fully interpret itsmeaning.

            e.  Whatis the standard error of the estimation?

            f.    Usethe F test to determine whether or not the regression model issignificant at a= 0.05.

            g.   Usethe t test to determine whether the slope of the regression modelis significant at a= 0.05.

            h.   Developa 99% confidence interval for the slope of the regressionmodel.

Answer & Explanation Solved by verified expert
4.3 Ratings (1022 Votes)

Regression Statistics
Multiple R 0.9197
R Square 0.8459
Adjusted R Square 0.8202
Standard Error 1.1994
Observations 8
ANOVA
df SS MS F Significance F
Regression 1 47.4 47.4 32.93 0.0012
Residual 6 8.6 1.4
Total 7 56.0
Coefficients Standard Error t Stat P-value Lower 99% Upper 99%
Intercept -10.42105 4.9711 -2.0963 0.0809 -28.8510 8.0089
X 0.78947 0.1376 5.7382 0.0006 0.2794 1.2996

a)

so, regression line is   Y? =   -10.4211   +   0.7895   *x

b)Predicted Y at X=   40   is                  
Y? =   -10.4211   +   0.7895   *   40   =   21.157894736842

answer: $21157895

c)

on average, increasing Advertising expenditure by $1000, predicted sales increase by $789474

d)R Square = 0.8459

about 84.59% of variation in observation of Y is explained by variable X

e)std error ,Se =    1.1994  

f)

F=32.93  

p value= 0.0012

g)

Ho:   ß1=   0
H1:   ß1 = 0

T test stat=5.7382

p value= 0.0012

h)

99% CI is

lower confidence limit = 0.279
upper confidence limit= 1.300


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