To predict the market share of one of their products, a manufacturer of consumer electronics products hired a market research company to conduct a study that relates market share in a particular geographic region (in %) to the average annual household income and the number of retail outlets per 100,000 residents. The results of a multiple regression model to predict market share from Household income (in thousands of dollars) and number of outlets per 100,000 residents are given below.
a) How much of the variation in market share can this model predict? Is this statistically significant?
b) Someone claims that each additional outlet will increase the market share by more than 1.5%, regardless of what the household income is. Perform the appropriate hypothesis test to check this claim with a 5% significance level.
c) What increase in market share would your model predict for every two additional retail outlets in a region where the annual household income is $75,000? Find a 95% confidence interval for this increase.
Transcribed Image Text:**SUMMARY OUTPUT**
*Regression Statistics*
- **Multiple R:** 0.80786648
- **R Square:** 0.65264825
- **Adjusted R Square:** 0.611783338
- **Standard Error:** 2.222508989
- **Observations:** 20
*ANOVA*
- **df**
- Regression: 2
- Residual: 17
- Total: 19
- **SS**
- Regression: 157.7777145
- Residual: 83.97228553
- Total: 241.75
- **MS**
- Regression: 78.88885724
- Residual: 4.939546207
- **F:** 15.9708714
- **Significance F:** 0.000124894
*Coefficients and Statistical Information*
- **Intercept**
- Coefficient: 5.098752286
- Standard Error: 4.359054223
- t Stat: 1.169692329
- P-value: 0.258263528
- Lower 95%: -4.09804822
- Upper 95%: 14.29555279
- **Household Income (in thousands of dollars)**
- Coefficient: 0.023411102
- Standard Error: 0.042677472
- t Stat: 0.548558788
- P-value: 0.59044049
- Lower 95%: -0.066630493
- Upper 95%: 0.113452697
- **Number of Outlets**
- Coefficient: 2.548132816
- Standard Error: 0.451959753
- t Stat: 5.637963998
- P-value: 2.95176E-05
- Lower 95%: 1.594581089
- Upper 95%: 3.501684544
This table provides the summary output of a statistical regression analysis, detailing the relationship between independent variables, such as household income and number of outlets, towards predicting the dependent variable. The analysis includes regression statistics, ANOVA results, and coefficient details with corresponding standard errors, t
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
