Problem 1 (Use R, please show your R codes and output) The dataset prostate (in R package "faraway") is from a study on 97 men with prostate cancer who were due to receive a radical prostatectomy. Fit a model with lpsa as the response variable (y) and Icavol as the predictor variable (x) and answer the following questions: a) ● ● b) c) ) Construct the analysis of variance table (ANOVA) and test for signifi- regression. ) Calculate the coefficient of determination (R²) and interpret it. ) Find a 95% confidence interval on the slope (B₁);

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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**Problem 1 (Use R, please show your R codes and output)**

The dataset *prostate* (in R package "faraway") is from a study on 97 men with prostate cancer who were due to receive a radical prostatectomy.

Fit a model with *lpsa* as the response variable (y) and *lcavol* as the predictor variable (x) and answer the following questions:

- **a)** Construct the analysis of variance table (ANOVA) and test for significance of regression.

- **b)** Calculate the coefficient of determination (R²) and interpret it.

- **c)** Find a 95% confidence interval on the slope (β₁);

- **d)** Find a 95% confidence interval on the mean *lpsa* when *lcavol* = 1.35;

- **e)** Calculate a 95% prediction interval of *lpsa* when *lcavol* = 1.35.
Transcribed Image Text:**Problem 1 (Use R, please show your R codes and output)** The dataset *prostate* (in R package "faraway") is from a study on 97 men with prostate cancer who were due to receive a radical prostatectomy. Fit a model with *lpsa* as the response variable (y) and *lcavol* as the predictor variable (x) and answer the following questions: - **a)** Construct the analysis of variance table (ANOVA) and test for significance of regression. - **b)** Calculate the coefficient of determination (R²) and interpret it. - **c)** Find a 95% confidence interval on the slope (β₁); - **d)** Find a 95% confidence interval on the mean *lpsa* when *lcavol* = 1.35; - **e)** Calculate a 95% prediction interval of *lpsa* when *lcavol* = 1.35.
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