Question

Steve Taylor is the owner of Home Plus, which is a chain of home improvement stores. He would like to investigate the relationship between month advertising and monthly sales. The table below shows the amount spent on advertising, in millions of dollars, over several months along with the corresponding sales, also in millions of dollars.

Month	Advertising ($ millions)	Sales ($ millions)
1	3	11
2	3	13
3	4	12
4	5	21
5	1	7

Show your work:

Determine the correlation coefficient for this data and interpret its meaning.

Perform a hypothesis test to determine if the population correlation coefficient is different than zero using ? = 0.05.

c) Calculate the regression line that will predict monthly sales based on the monthly advertising.

d) Interpret the slope of the regression equation.

e)   Predict the average number of sales for a month with $2 million spent on advertising.

f) Calculate the total sum of squares, sum of squares error, and sum of squares regression.

g) Calculate the coefficient of determination.

h) Interpret the meaning of the coefficient of determination.

i) Test the significance of the coefficient of determination using ? = 0.05.

j) Calculate the standard error of the estimate.

k) Calculate the 95% confidence interval for the average sales for a month where $4 million was spent on advertising.

Answer 1

a) Correlation coefficient r is calculated as

In our data x=Advertising and y=Sales

We calculate the various sums in the below table

Month	Advertising (x)	Sales (y)	X^2	y2	xy
1	3	11	9	121	33
2	3	13	9	169	39
3	4	12	16	144	48
4	5	21	25	441	105
5	1	7	1	49	7
Total ?	16	64	60	924	232
Total^2	256	4096

Putting the values above in our formaula we get r = 0.8956677

b) Null hypothesis: Ho:

Alternate hypothesis: Ha:

Using the table of critical values, with and df=3 (n-2)

We get the critical value of 0.878

Since, r calculated value 0.8957 > critical value 0.878, we reject the null hypothesis and conclude that the population correlation coefficient is significant.

c) The regression line equation is as below

where y= Sales and x=Advertising.

d) The slope of the regression line is 2.909. When Advertising spend is zero, the sales in a month would be 2.909 $ million

e) When advertising spend is 2 $ million,

y = 2.909 + 3.091 * 2 = 9.091

Thus the sales would be 9.091$ million when advertising spend is 2 $ million.