8. Use the multiple regression output shown to answer the following questions. The regression equation is: Y = 9.77 0.775X1 + 0.062X2 - 0.221X3 Predictor Coef SE Coef T P Constant 9.771 7.132 1.37 0.184 X1 0.7747 0.3201 2.42 0.025 X2 0.0642 0.1686 0.37 0.716 X3 -0.2214 0.1730 -1.28 0.214 S = 5.04975 R - Sq = 14.9% R - Sq (adj) = 2.8% Analysis of Variance Source DF SS MS F P Regression 3 94.1 31.35 1.23 0.322 Residual Error 21 535.5 25.5 Total 24 629.6 (a) What is R2 for this model? Do we expect to increase, decrease, or remain the same if we eliminate the variable chosen in part (a)? What type of change in would indicate that removing the variable in part (a) was a GOOD idea? What type of change in would indicate that removing the variable in part (a) was a BAD idea? b) What is the p-value for ANOVA for the original 3-predictor model? Is the p-value most likely to increase, decrease, or remain the same if we eliminate the variable chosen in part (a)? What type of change in the p-value for ANOVA would indicate that removing the variable in part (a) was a GOOD idea? What type of change in the p-value for ANOVA would indicate that removing the variable in part (a) was a BAD idea? c) What is the F-statistic from ANOVA for this model? Is the F-statistic most likely to increase, decrease, or remain the same if we eliminate the variable chosen in part (a)? What type of change in the F-statistic for ANOVA would indicate that removing the variable in part (a) was a good idea?
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.
8. Use the multiple regression output shown to answer the following questions.
The regression equation is:
Y = 9.77 0.775X1 + 0.062X2 - 0.221X3
| Predictor | Coef | SE Coef | T | P |
| Constant | 9.771 | 7.132 | 1.37 | 0.184 |
| X1 | 0.7747 | 0.3201 | 2.42 | 0.025 |
| X2 | 0.0642 | 0.1686 | 0.37 | 0.716 |
| X3 | -0.2214 | 0.1730 | -1.28 | 0.214 |
S = 5.04975 R - Sq = 14.9% R - Sq (adj) = 2.8%
| Analysis of Variance | |||||
| Source | DF | SS | MS | F | P |
|---|---|---|---|---|---|
| Regression | 3 | 94.1 | 31.35 | 1.23 | 0.322 |
| Residual Error | 21 | 535.5 | 25.5 | ||
| Total | 24 | 629.6 |
(a) What is R2 for this model? Do we expect to increase, decrease, or remain the same if we eliminate the variable chosen in part (a)? What type of change in would indicate that removing the variable in part (a) was a GOOD idea? What type of change in would indicate that removing the variable in part (a) was a BAD idea?
b) What is the p-value for ANOVA for the original 3-predictor model?
Is the p-value most likely to increase, decrease, or remain the same if we eliminate the variable chosen in part (a)? What type of change in the p-value for ANOVA would indicate that removing the variable in part (a) was a GOOD idea? What type of change in the p-value for ANOVA would indicate that removing the variable in part (a) was a BAD idea?
c) What is the F-statistic from ANOVA for this model? Is the F-statistic most likely to increase, decrease, or remain the same if we eliminate the variable chosen in part (a)? What type of change in the F-statistic for ANOVA would indicate that removing the variable in part (a) was a good idea?
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