A large Italian restaurant chain utilized three types of marketing. These were s

Question

A large Italian restaurant chain utilized three types of marketing. These were social media marketing (Facebook, Twitter etc.), direct email marketing, and local television advertisements. The marketing manager needed to plan a budget for the following marketing year and wanted to determine which method of marketing was most effective. To determine this, the manager collected one week's data from one-hundred randomly selected restaurants. For each restaurant, the following variables were recorded Weekly gross sales .Weekly expenditures on social media marketing Weekly expenditures on direct email marketing Weekly expenditures on television commercials All variables were recorded in thousands of dollars. 1. Find the regression equation 2. What are the coefficient of determination and the coefficient of determination adjusted for degrees of freedom? What do these statistics tell you about the regression equation? 3. What does the standard error of estimate tell you about the regression model? 4. Test the validity of the model 5. Which independent variables are linearly related to weekly gross sales in this model? Explain. 6. Compute the 95% interval of the week's gross sales if a local store spent $800 on social media marketing, $1,200 on direct email marketing, and $2,000 on television commercials 7. Calculate the 95% interval of the mean weekly gross sales for all stores that spend $800 on social media marketing, $1,200 orn direct email marketing, and $2,000 on television commercials.

Explanation / Answer

Regression Analysis: Sales versus Social, Email, Television

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 3 34.104 11.3679 1.70 0.198
Social 1 0.735 0.7345 0.11 0.744
Email 1 31.150 31.1500 4.65 0.043
Television 1 0.936 0.9355 0.14 0.712
Error 21 140.560 6.6933
Total 24 174.663

Model Summary

S R-sq R-sq(adj) R-sq(pred)
2.58714 19.53% 8.03% 0.00%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant 12.31 4.70 2.62 0.016
Social 0.57 1.72 0.33 0.744 1.03
Email 3.32 1.54 2.16 0.043 1.04
Television 0.73 1.96 0.37 0.712 1.03

Regression Equation

Sales = 12.31 + 0.57 Social + 3.32 Email + 0.73 Television
Prediction for Sales

Regression Equation

Sales = 12.31 + 0.57 Social + 3.32 Email + 0.73 Television

Variable Setting
Social 800
Email 1200
Television 2000

Fit SE Fit 95% CI 95% PI
5916.58 4523.78 (-3491.12, 15324.3) (-3491.12, 15324.3)

1)
The Regression Equation is,
Sales = 12.31 + 0.57 Social + 3.32 Email + 0.73 Television
2)
Coefficient of Determination R2 Square = 19.53%  
R2 square adjusted = 8.03%
R2 and R2 adjusted is very small indicates over all validity of model is not good.

3)
Standard Error of estimate is 2.58714 which measure accuracy of the predictions made with regression line.
4)
F =1.70 corresponding p-value =0.198 < 0.05 indicates model is not vallied.

Variable Setting
Social 800
Email 1200
Television 2000

Fit SE Fit 95% CI 95% PI
5916.58 4523.78 (-3491.12, 15324.3) (-3491.12, 15324.3)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.