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Hey can you please help me with question 3 and 4, I tried to do it manually, but couldn't do it on minitab. Could you please show me how to do it on
4.50
a. Use each of the 4 independent variables, one at a time and obtain 4 Simple Linear Regression (SLR) Equations for the response variable, 'Selling Price'. Rank these 4 SLR equations in 'Descending Order' from the 'Best' to the 'Worst'. Explain what specific criteria you use in this ranking.
b. Now use all the 4 independent variables and all the data to obtain 1 Full Multiple Linear Regression (MLR) equation for all the independent/explanatory variables.
c. Manually calculate the R2 and R2Adj for this MLR equation and comment on the quality of the regression. Explain the significance of R2.
d. By simply observing the MiniTab printout and without doing any formal analysis, comment on which of the parameters, β0, β1, β2, β3, β4 are significant. What specific numerical criterion did you use? Explain briefly.
e. Now drop the worst performing independent variable and use the remaining three independent variables, to obtain the new 'Best' MLR equation.
f. Manually calculate the R2 and R2Adj for this new 'Best' MLR equation and comment on the quality of this regression. Use "Best Subset" approach to justify if this 'Best' Multiple Regression is in fact the 'Best'!
g. For this 'Best' MLR equation, plot the 4 standardized residuals and comment on at least 2 different plots. Justify the aptness of this 'Best' MLR equation by stating if the assumptions for this regression model have been met or not. Do you see any possible problems?
h. Explain why the 'Best' MLR equation is better than the MLR equation with 4 independent variables.
i. In part 'b' above, you obtained your "Full" MLR equation with all the data. Now, drop the most 'unusual observation' (just one observation!) and find the new equation and specify what it would be. Is it better than the "Full" MLR equation?
For this Question, use the 'Best' MLR equation that you have obtained in Qu.#3, part 'e'.
a. Manually conduct the Hypothesis Test on 'β1' at the 5% 'Level of Significance'. Use 'Critical Value'of 't' to reach your conclusion. Also calculate the p-Value and based on it, justify your conclusion.
b. Manually conduct the Hypothesis Test on 'Significance of Regression' at the 5% 'Level of Significance'. Use 'Critical Value' of 'F' to reach your conclusion. Also calculate the p-Value and based on it, justify your conclusion.
c. Manually Obtain the 99% Confidence Interval for the 'Selling Price' of the house when the area is 4000 square feet, and there are 2 floors, 5 bedrooms and 3 bath rooms. What does this Interval mean? Explain in brief.
d. Manually obtain the 99% Prediction Interval for the 'Selling Price' when the area is 4000 square feet, and there are 2 floors, 5 bedrooms and 3 bath rooms. What does this Interval mean? Explain in brief.
e. In this 'Best' MLR, the VIF for predictor variable 'SqFt' is 1.879. Explain how this number is calculated and demonstrate with actual calculations. What is the significance of this VIF number?
f. At the end of the analysis, the Real Estate Company realized that it should include "Neighbourhood" as an additional predictor variable with "Poor", "Middle Class" and "Upscale" as possible categories. What kind of variable/s would this/these be and how should these categories be coded? Explain in brief.
