Shown below is a portion of the computer output for a regression analysis relati
ID: 3245216 • Letter: S
Question
Shown below is a portion of the computer output for a regression analysis relating sales (Y in millions of dollars) and advertising expenditure (X in thousands of dollars).
Predictor
Coefficient
Standard Error
Constant
4.00
0.800
X
0.12
0.45
Analysis of Variance
SOURCE
DF
SS
Regression
1
1,400
Error
17
3,600
a. Perform a t test and determine whether or not advertising and sales are related. Let = 0.05.
b.Compute the coefficient of determination
c. Use the estimated regression equation and predict sales for an advertising expenditure of $4,500. Give your answer in dollars.
Predictor
Coefficient
Standard Error
Constant
4.00
0.800
X
0.12
0.45
Explanation / Answer
a.
test statistic t = Coeff. of X/ Std error of X = 0.12/0.45 = 0.2667
Degree of freedom = 17
p-value for t = 0.2667 and degree of freedom = 17 is 0.3964
As the p-value is greater than the significance level = 0.05, we fail to reject the null hypothesis and conclude that coefficient of X is zero and advertising and sales are not related.
b.
Total sum of squares, SST = SS for Regression + SS for Error = 1400 + 3600 = 5000
coefficient of determination = SSR/SST = 1400/5000 = 0.28
c.
Regression equation is, sales = 4.00 + 0.12X
advertising expenditure = $4,500 = $4.5 thousand
sales = 4.00 + 0.12 * 4.5 = $4.54 millions = $4540000
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