[3 points] (f) Fit a multiple regression model using all 3 predictors. Describe your results. For which predictors

can we reject the null hypothesis H0 : j = 0 ?

[2 points] (g) Given a new data point (zn = 12, dis = 4, lstat = 15), predict the response medv using the

multiple regression model fitted in (f).

[3 points] (h) Calculate and compare the 95% confidence and prediction intervals for this new data point.

Plz use R-studio~

This question needs the Boston data set in package MASS. Use medv column as the response, and other variables are the predictors. You can use ?Boston to see the details of this dataset. 2 point] (a) Create a new data set Boston2, which is a subset of Boston with the columns: medv, zn, dis, lstat. How many rows and columns in the Boston2 data set. We only use this Boston2 data set to do all the following questions 1 point] (b) Describe briefly what these 4 variables chosen in our data set Boston2 represent. (hint: ?Boston) 2 points (c) For the predictor lstat, fit a simple linear regression model to predict the response medv. Comment on the model obtained. Is there a statistically significant relationship between the predictor and the response? Is the relationship positive or negtive? 2 points] (d) Create the residual plot for the simple lincar regression model fitted above (x-axis: fitted y y-axis: residuals). According to the residual plot, do you think the relationship between lstat and response medv is linear or no n-linear? Explain [2 points (e) For the predictor Istat, fit a model with polynomial terms: m edu = 30 +Alstat +Alstat2+ Bilstat3 . According to your results, is there evidence of non-linear association between medv and lstat? Comment on your results. This question needs the Boston data set in package MASS. Use medv column as the response, and other variables are the predictors. You can use ?Boston to see the details of this dataset. 2 point] (a) Create a new data set Boston2, which is a subset of Boston with the columns: medv, zn, dis, lstat. How many rows and columns in the Boston2 data set. We only use this Boston2 data set to do all the following questions 1 point] (b) Describe briefly what these 4 variables chosen in our data set Boston2 represent. (hint: ?Boston) 2 points (c) For the predictor lstat, fit a simple linear regression model to predict the response medv. Comment on the model obtained. Is there a statistically significant relationship between the predictor and the response? Is the relationship positive or negtive? 2 points] (d) Create the residual plot for the simple lincar regression model fitted above (x-axis: fitted y y-axis: residuals). According to the residual plot, do you think the relationship between lstat and response medv is linear or no n-linear? Explain [2 points (e) For the predictor Istat, fit a model with polynomial terms: m edu = 30 +Alstat +Alstat2+ Bilstat3 . According to your results, is there evidence of non-linear association between medv and lstat? Comment on your results