Grinfield Service Company’s marketing director is interested in analyzing the re
ID: 1142052 • Letter: G
Question
Grinfield Service Company’s marketing director is interested in analyzing the relationship between her company’s sales and the advertising dollars spent. In the course of her analysis, she selected a random sample of 20 weeks and recorded the sales for each week and the amount spent on advertising. The summary statistics are for 20 observations.
Cov(x,y)=170436.10
a. Find the correlation coefficient between sales and advertising. What does it mean? b. Find the least squares line that shows how weekly sales ( y ) is related to advertising dollars ( x ). c. According to the least squares line, how is weekly sales related to advertising dollars? What does the intercept mean?
Hilmer. Practical Econometrics (The Mcgraw-hill/Irwin Series in Economics) (Page 101). McGraw-Hill Education. Kindle Edition.
sales advertising sample mean 3353 298 standard dev 1408 133Explanation / Answer
a.
Correlation = Cov(X,Y)/Standard dev(Sales)*Standard dev(Advertising)
= 170436.10/(1408*133)
= 0.9101
It means that sales and advertising are strongly and positively correlated in a linear manner. That is, if advertising goes up, then Sales also goes up.
b.
The regression model we want to estimate looks like -
Sales = b0 + b1*Advertising + e
Formula for slope coefficient,b1 =correlation coefficient*Standard dev(Sales)/Standard dev(Advertising)
= 0.9101*1408/133
= 9.63
To find the intercept term we use the below result -
Mean Sales = b0 + b1*Mean Advertising
then b0 = Mean sales - b1*Mean Advertising, where
mean sales =3353
mean advertising= 298
b1 = 9.63
b0 = 3353 - 9.63*298
b0 = 483.26
The estimated equation is -
Sales = 483.26 +9.63*Advertising
1. According to least squares, a $1 increase in advertising expenditure results in $9.63 increase in Sales.
2. The intercept term tells us the average sales if the advertising expenditure is 0.
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