As a marketing manager for TriFood, you want to determine whether store Sales (# sold in one month) of TriPower bars are related to price (in cents) of TriPower bars and in-store promotional expenditures (in dollars) for TriPower bars. You conduct a multiple regression analysis with store Sales (Y) as the response variable, and Price (X1) and Promotion (X2) as explanatory variables. Use the pictured Excel regression output below to answer the questions. a) Interpret the value for R square. Interpret the estimated coefficient for price. b) State the hypotheses for assessing the statistical significance of the overall regression equation. Does the model overall fit the data (yes or no?) f) An external consultant to TriFoods believes that for every $1 increase in promotional expenditures, sales will increase by 4.7 units. Test the consultant's hypothesis at a 5% significance level using both approaches (tcalc vs tcrit and p-value vs a).
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
As a marketing manager for TriFood, you want to determine whether store Sales (# sold in one month) of TriPower bars are related to price (in cents) of TriPower bars and in-store promotional expenditures (in dollars) for TriPower bars. You conduct a multiple
a) Interpret the value for R square. Interpret the estimated coefficient for price.
b) State the hypotheses for assessing the statistical significance of the overall regression equation. Does the model overall fit the data (yes or no?)
f) An external consultant to TriFoods believes that for every $1 increase in promotional expenditures, sales will increase by 4.7 units. Test the consultant's hypothesis at a 5% significance level using both approaches (tcalc vs tcrit and p-value vs a).
![### Regression Analysis Results
The table below presents the results of the regression analysis conducted for the dataset.
#### Regression Statistics:
- **Multiple R**: 0.8705
- **R Square**: 0.7577
- **Adjusted R Square**: 0.7421
- **Standard Error**: 638.0653
- **Observations**: 34
#### ANOVA Table:
| Source | df | SS | MS | F | Significance F |
|------------------|----|---------------|--------------|----------|-----------------|
| Regression | 2 | 39472730.8 | 19736365.4 | 48.4771 | 2.86258E-10 |
| Residual | 31 | 12620946.7 | 407127.3 | | |
| Total | 33 | 52093677.4 | | | |
#### Coefficients Table:
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% |
|--------------|----------------|---------|---------|------------|------------|
| Intercept | 5837.5208 | 628.1502| 9.2932 | 0.0000 | 4556.3999 | 7118.6417 |
| Price | -53.2173 | 6.8522 | -7.7654 | 0.0000 | -67.1925 | -39.2421 |
| Promotion | 3.6131 | 0.6852 | 5.2728 | 0.0000 | 2.2155 | 5.0107 |
### Explanation of Terms:
1. **Multiple R**: This is the correlation coefficient that measures the strength and direction of a linear relationship between the variables.
2. **R Square**: The proportion of variance in the dependent variable that is predictable from the independent variables.
3. **Adjusted R Square**: Adjusted R Square corrects R Square for the number of predictors in the model.
4. **Standard Error**: An estimate of the standard deviation of the error term.
5. **Observations**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe62ffb3d-7efc-4be2-adcf-bca36514e923%2F8e198579-0040-495a-8b44-1176ab6dc430%2F37qxfji.png&w=3840&q=75)
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