Refrigerator prices are affected by characteristics such as whether or not the refrigerator is on sale, whether or not it is listed as a Sub-Zero brand, the number of doors (one door or two doors), and the placement of the freezer compartment (top, side, or bottom). The table below shows the regression output from a regression model using the natural log of price as the dependent variable. The model was developed by the Bureau of Labor Statistics. Variable Coefficient Standard Error t Statistic Intercept 5.2700 0.12679 41.56 Sale price −0.0741 0.0239 −3.10 Sub-Zero brand 1.2056 0.1387 8.69 Total capacity (in cubic ft) 0.07588 0.00626 12.12 Two-door, freezer on bottom 0.05354 0.07222 0.74 Two-door, side freezer Base Two-door, freezer on top −0.3031 0.03846 −7.88 One door with freezer −0.7693 0.1337 −5.75 One door, no freezer −0.8381 0.1529 −5.48 (a) Write the regression model, being careful to exclude the base indicator variable. (Negative amounts should be indicated by a minus sign. Round your answers to 4 decimal places.) ln(Price) = + SalePrice + Sub-Zero + Capacity + 2DoorFzBot + 2DoorFzTop + 1DoorFz + 1DoorNoFz (b) Find the p-value for each coefficient, using 302 degrees of freedom. Using an α = .01, which predictor variable(s) are not significant predictors? (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 4 decimal places.) p-value SalePrice Sub-Zero Capacity 2DoorFzBot 2DoorFzTop 1DoorFz 1DoorNoFz (c) By how much does the natural log of refrigerator price decrease from a two-door, side freezer model to a two-door, top freezer model? (Round your answer to 4 decimal places.) The natural log of the price decreases by
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.
Refrigerator prices are affected by characteristics such as whether or not the refrigerator is on sale, whether or not it is listed as a Sub-Zero brand, the number of doors (one door or two doors), and the placement of the freezer compartment (top, side, or bottom). The table below shows the regression output from a regression model using the natural log of price as the dependent variable. The model was developed by the Bureau of Labor Statistics.
| Variable | Coefficient | Standard Error | t Statistic | |||||
| Intercept | 5.2700 | 0.12679 | 41.56 | |||||
| Sale price | −0.0741 | 0.0239 | −3.10 | |||||
| Sub-Zero brand | 1.2056 | 0.1387 | 8.69 | |||||
| Total capacity (in cubic ft) | 0.07588 | 0.00626 | 12.12 | |||||
| Two-door, freezer on bottom | 0.05354 | 0.07222 | 0.74 | |||||
| Two-door, side freezer | Base | |||||||
| Two-door, freezer on top | −0.3031 | 0.03846 | −7.88 | |||||
| One door with freezer | −0.7693 | 0.1337 | −5.75 | |||||
| One door, no freezer | −0.8381 | 0.1529 | −5.48 | |||||
(a) Write the regression model, being careful to exclude the base indicator variable. (Negative amounts should be indicated by a minus sign. Round your answers to 4 decimal places.)
ln(Price) = + SalePrice + Sub-Zero + Capacity + 2DoorFzBot + 2DoorFzTop + 1DoorFz + 1DoorNoFz
(b) Find the p-value for each coefficient, using 302 degrees of freedom. Using an α = .01, which predictor variable(s) are not significant predictors? (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 4 decimal places.)
| p-value | |
| SalePrice | |
| Sub-Zero | |
| Capacity | |
| 2DoorFzBot | |
| 2DoorFzTop | |
| 1DoorFz | |
| 1DoorNoFz | |
(c) By how much does the natural log of refrigerator price decrease from a two-door, side freezer model to a two-door, top freezer model? (Round your answer to 4 decimal places.)
The natural log of the price decreases by
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