Home Sale Prices. Regarding the relationship between the sale price of a home and the predictor variables size in square feet and type of roof (tile or non-tile). In that exercise, we considered the regression of price on size and roof, the indicator variable for type of roof. a. Obtain a plot of price versus size with different plot symbols for homes having a tile roof and for homes having a non-tile roof. Based on this plot, does it appear that roof is a useful predictor variable? Explain your answer. b. Obtain the regression analysis of price on size and roof. Conduct the t-tests for the individual utility of the two predictor variables at the 5% level of significance. Interpret your results. c. Based on the output in part (b), obtain the individual regression equations relating price to size for homes having tile roofs and for homes having non-tile roofs. d. Obtain plots of residuals versus fitted values, residuals versus size, residuals versus roof, and a normal probability plot of the residuals. Perform a residual analysis to assess the appropriateness of the regression equation, constancy of the conditional standard deviations, and normality of the conditional distributions. Check for outliers and influential observations. e. Provide a scatterplot of price versus size with the individual regression lines for homes with tile roofs and homes with non-tile roofs. Based on this plot and your residual analysis from part (d), do you feel that this model fits the data well? Explain your answer. f. To check for possible interaction between the two predictor variables, perform the regression analysis of price on size, roof, and . Is there an interaction between size and, that is, is the cross-product term roof. size a useful predictor variable in the regression equation that also contains size and roof? Use α = 0.05.
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.
Home Sale Prices. Regarding the relationship between the sale price of a home and the predictor variables size in square feet and type of roof (tile or non-tile). In that exercise, we considered the regression of price on size and roof, the indicator variable for type of roof.
a. Obtain a plot of price versus size with different plot symbols for homes having a tile roof and for homes having a non-tile roof. Based on this plot, does it appear that roof is a useful predictor variable? Explain your answer.
b. Obtain the
c. Based on the output in part (b), obtain the individual regression equations relating price to size for homes having tile roofs and for homes having non-tile roofs.
d. Obtain plots of residuals versus fitted values, residuals versus size, residuals versus roof, and a normal probability plot of the residuals. Perform a residual analysis to assess the appropriateness of the regression equation, constancy of the conditional standard deviations, and normality of the conditional distributions. Check for outliers and influential observations.
e. Provide a
f. To check for possible interaction between the two predictor variables, perform the regression analysis of price on size, roof, and . Is there an interaction between size and, that is, is the cross-product term roof. size a useful predictor variable in the regression equation that also contains size and roof? Use α = 0.05.
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