(40 pts) 1. The dataset prostate (in R package faraway) is from a study on 97...

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(40 pts) 1. The dataset prostate (in R package faraway") is from a study on 97 men with prostate cancer who were due to receive radical prostatectomy. Fit a model with Ipsa as the response variable (y) and Icavol as the predictor variable (x) and answer the following questions (show your R codes): a) Make a scatter plot of the two variables (Ipsa and Icavol). b) From the plot in (a), is there a linear relationship between Ipsa and Icavol? Is it positive or negative? c) Report the fitted regression model. d) Interpret the intercept and slope. e) Plot the fitted regression line. f) Predict the response variable when the predictor x = = 3. g) Find SST, SSE and SSR. h) What is the value of the coefficient determination? Interpret it. Bonus question (10 pts) For part (e) above, can you predict the response variable when x = 7? Show your codes and explain why. (40 pts) 1. The dataset prostate (in R package faraway") is from a study on 97 men with prostate cancer who were due to receive radical prostatectomy. Fit a model with Ipsa as the response variable (y) and Icavol as the predictor variable (x) and answer the following questions (show your R codes): a) Make a scatter plot of the two variables (Ipsa and Icavol). b) From the plot in (a), is there a linear relationship between Ipsa and Icavol? Is it positive or negative? c) Report the fitted regression model. d) Interpret the intercept and slope. e) Plot the fitted regression line. f) Predict the response variable when the predictor x = = 3. g) Find SST, SSE and SSR. h) What is the value of the coefficient determination? Interpret it. Bonus question (10 pts) For part (e) above, can you predict the response variable when x = 7? Show your codes and explain why.