The information below represents the relationship between the selling price (Y, in $1,000) of a home, the square footage of the home (), and the number of rooms in the home (). The data represents 60 homes sold in a particular area of East Lansing, Michigan and was analyzed using multiple linear regression and simple regression for each independent variable. The first two tables relate to the multiple regression analysis. Summary measures Multiple R 0.9408 R-Square 0.8851 Adj R-Square 0.8660 StErr of Estimate 20.8430 Regression coefficients Coefficient Std Err t-value p-value Constant -13.9705 49.1585 -0.2842 0.7811 Size 7.4336 1.0092 7.3657 0.0000 Number of Rooms 5.3055 8.2767 0.6410 0.5336 The following table is for a simple regression model using only size. (= 0.8812) Coefficient Std Err t-value p-value Constant 14.771 19.691 0.7502 0.4665 Size 7.816 0.796 9.8190 0.0000 The following table is for a simple regression model using only number of rooms. (= 0.3657) Coefficient Std Err t-value p-value Constant -93.460 108.269 -0.8632 0.4037 Number of Rooms 41.292 15.082 2.7379 0.0169 (A) Use the information related to the multiple regression model to determine whether each of the regression coefficients are statistically different from 0 at a 5% significance level. Summarize your findings. (B) Test at the 5% significance level the relationship between Y and X in each of the simple linear regression models. How does this compare to your answer in part (A)? Explain. (C) Is there evidence of multicollinearity in this situation? Explain why or why no
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.
The information below represents the relationship between the selling price (Y, in $1,000) of a home, the square footage of the home (), and the number of rooms in the home (). The data represents 60 homes sold in a particular area of East Lansing, Michigan and was analyzed using multiple linear regression and simple regression for each independent variable. The first two tables relate to the multiple
| Summary measures | |
| Multiple R |
0.9408 |
| R-Square |
0.8851 |
| Adj R-Square |
0.8660 |
| StErr of Estimate |
20.8430 |
| Regression coefficients | ||||
|
Coefficient |
Std Err |
t-value |
p-value |
|
| Constant |
-13.9705 |
49.1585 |
-0.2842 |
0.7811 |
| Size |
7.4336 |
1.0092 |
7.3657 |
0.0000 |
| Number of Rooms |
5.3055 |
8.2767 |
0.6410 |
0.5336 |
The following table is for a simple regression model using only size. (= 0.8812)
| Coefficient | Std Err | t-value | p-value | |
| Constant | 14.771 | 19.691 | 0.7502 | 0.4665 |
| Size | 7.816 | 0.796 | 9.8190 | 0.0000 |
The following table is for a simple regression model using only number of rooms. (= 0.3657)
| Coefficient | Std Err | t-value | p-value | |
| Constant | -93.460 | 108.269 | -0.8632 | 0.4037 |
| Number of Rooms | 41.292 | 15.082 | 2.7379 | 0.0169 |
(A) Use the information related to the multiple regression model to determine whether each of the regression coefficients are statistically different from 0 at a 5% significance level. Summarize your findings.
(B) Test at the 5% significance level the relationship between Y and X in each of the simple linear regression models. How does this compare to your answer in part (A)? Explain.
(C) Is there evidence of multicollinearity in this situation? Explain why or why not.
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