A small Internet company wants to determine how the money they spend on Google A
ID: 3218209 • Letter: A
Question
A small Internet company wants to determine how the money they spend on Google Adwords impacts their monthly revenue. Over 6 consecutive months, they vary the amount they spend on their Adwords campaign (in $) and record the associated revenue (in $) for each month. The data is shown below.
a) Develop a regression equation for predicting monthly revenue based on the amount spent with Adwords. What is the y-intercept? Give your answer to two decimal places.
b) What is the proper interpretation of the y-intercept in the regression equations?
A.The y-intercept describes the expected decrease in revenue for each additional dollar spent on Adwords.
B.The y-intercept describes the expected revenue if the company does not spend any money in a given month on Adwords.
C.The y-intercept describes the expected revenue if the company spends $25 in a given month on Adwords.
D. The y-intercept describes the expected increase in revenue for each additional dollar spent on Adwords.
c) What is the sample correlation between these two variables? Give your answer to two decimal places.
d) What is the slope of your regression equation? Give your answer to two decimal places.
e) Using a 0.05 level of significance, does this regression equation appear to have any value for predicting revenue based on Adwords expenditures?
A.No because there is a significant linear relationship between the two quantities.
B. No because there is not a significant linear relationship between the two quantities.
C. Yes because there is not a significant linear relationship between the two quantities.
D. Yes because there is a significant linear relationship between the two quantities.
Explanation / Answer
Regression output from excel
The regression equation is revenue = (0.03* adwords) + 96.48
b) the proper interpretation of the y-intercept in the regression equations
D. The y-intercept describes the expected increase in revenue for each additional dollar spent on Adwords.
For one dollar change in revenue there will be 0.03 times change in adwords.
c) Sample correlation coefficient between two variables is 0.04 (Multiple R from the output).
d) the slope of regression equation = 0.03 (Coefficient of adwords).
e) Using a 0.05 level of significance, the regression equation appear to have any value for predicting revenue based on Adwords expenditures:
From the ANOVA table the F-test statistic is 0.005618 with p-value of 0.9439.
Since the p-value is not less than 0.05 we do not reject the null hypothesis that the regression parameters are zero at significance level 0.05.
Conclude that the parameters are jointly statistically insignificant at significance level 0.05.
C. Yes because there is not a significant linear relationship between the two quantities.
SUMMARY OUTPUT Regression Statistics Multiple R 0.037449857 R Square 0.001402492 Adjusted R Square -0.248246885 Standard Error 52.25456977 Observations 6 ANOVA df SS MS F Significance F Regression 1 15.33975386 15.33975 0.005618 0.943851476 Residual 4 10922.16025 2730.54 Total 5 10937.5 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 96.4784793 214.8181166 0.449117 0.676606 -499.9522289 692.9091875 -499.9522289 692.9091875 X Variable 1 0.031466162 0.41981587 0.074952 0.943851 -1.134129556 1.197061879 -1.134129556 1.197061879