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1) The data set "Boston" contains medv (median value of owner-occupied homes in $1000s) and 1stat (lower status of the population (percent)) in n=506 different census tracts in Boston. We wish to predict a value of medv using 1stat as a covariate. Use the R code to load the data set and create a plot of 1stat and medv. 11brary (ISLR2) head (Boston) ## crim zn indus chas nox ## 1 0.00632 18 2.31 ## 2 0.02731 0 7.07 ## 3 0.02729 0 7.07 # # 4 0.03237 0 2.18 ## 5 0.06905 0 2.18 ## 6 0.02985 0 2.18 15.3 4.98 24.0 rm age dis rad tax ptratio 1stat medv 0 0.538 6.575 65.2 4.0900 1 296 0 0.469 6.421 78.9 4.9671 0 0.469 7.185 61.1 4.9671 0 0.458 6.998 45.8 6.0622 0 0.458 7.147 54.2 6.0622 0 0.458 6.430 58.7 6.0622 2 242 2 242 3 222 3 222 3 222 17.8 17.8 18.7 18.7 18.7 9.14 21.6 4.03 34.7 2.94 33.4 5.33 36.2 5.21 28.7

1) The data set "Boston" contains medv (median value of owner-occupied homes in $1000s) and 1stat (lower status of the population (percent)) in n=506 different census tracts in Boston. We wish to predict a value of medv using 1stat as a covariate. Use the R code to load the data set and create a plot of 1stat and medv. 11brary (ISLR2) head (Boston) ## crim zn indus chas nox ## 1 0.00632 18 2.31 ## 2 0.02731 0 7.07 ## 3 0.02729 0 7.07 # # 4 0.03237 0 2.18 ## 5 0.06905 0 2.18 ## 6 0.02985 0 2.18 15.3 4.98 24.0 rm age dis rad tax ptratio 1stat medv 0 0.538 6.575 65.2 4.0900 1 296 0 0.469 6.421 78.9 4.9671 0 0.469 7.185 61.1 4.9671 0 0.458 6.998 45.8 6.0622 0 0.458 7.147 54.2 6.0622 0 0.458 6.430 58.7 6.0622 2 242 2 242 3 222 3 222 3 222 17.8 17.8 18.7 18.7 18.7 9.14 21.6 4.03 34.7 2.94 33.4 5.33 36.2 5.21 28.7

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please do the following questions in the image with R coding 

6) State the assumptions of the linear regression model. 7) L Create the histogram of the residual and the residual plot. Comment assumption of the linear regression model is satisfied or not. 8) Use 1m () function in R and fit the regression model in 3) and use summary() function to display output of 1m () function. Again we use the model in 3). Use the output from 8) and do the test of hypothesis Ho: B=0 vs H₁:8 +0. Use a = 0.05. Then construct the 95% confidence interval of B.
Transcribed Image Text:6) State the assumptions of the linear regression model. 7) L Create the histogram of the residual and the residual plot. Comment assumption of the linear regression model is satisfied or not. 8) Use 1m () function in R and fit the regression model in 3) and use summary() function to display output of 1m () function. Again we use the model in 3). Use the output from 8) and do the test of hypothesis Ho: B=0 vs H₁:8 +0. Use a = 0.05. Then construct the 95% confidence interval of B.
Q1. 1) The data set "Boston" contains medv (median value of owner-occupied homes in $1000s) and 1stat (lower status of the population (percent)) in n-506 different census tracts in Boston. We wish to predict a value of medv using 1stat as a covariate. Use the R code to load the data set and create a plot of 1stat and medv. 11brary (ISLR2) head (Boston) ## crim zn indus chas ## 1 0.00632 18 2.31 ## 2 0.02731 07.07 # # 3 0.02729 0 7.07 # # 4 0.03237 0 2.18 # # 5 0.06905 0 2.18 # # 6 0.02985 0 2.18 nox rm age 0 0.538 6.575 65.2 4.0900 0 0.469 6.421 78.9 4.9671 0 0.469 7.185 61.1 4.9671 0 0.458 6.998 45.8 6.0622 0 0.458 7.147 54.2 6.0622 0 0.458 6.430 58.7 6.0622 2) Szz, Syy, Sry are defined by 71 ST1 = (T-F)², Syy-i-)², Szy=(Ti-T) (Vi-T). i=1 i=1 9.14 21.6 dis rad tax ptratio 1stat medv 1 296 15.3 4.98 24.0 2 242 17.8 2 242 17.8 3 222 18.7 2.94 33.4 3 222 18.7 5.33 36.2 3 222 18.7 5.21 28.7 4.03 34.7 = The least square estimate of a and 3 are i=1 Use the definition and using R, calculate Sr. Syy, Szy- 3) 1 The equation of the linear regression is y = a + Br+e. 3= Szy and & = 7-8. SII Use the formula given above and calculate the least square estimate of a and 3 (in R). The predicted value of y are calculate by the formula 91 = a + 3x₂ where à and 3 are the least square estimate of a and 3. Use the formula and calculate the predicted values ; (in R). Print the first 5 predicted values. The residual sum of squares (RSS) is defined by n Rss = Σ(m - 0;). i=1 Use the definition, and compute the RSS in R. Then compute RSS RSE = Vn-
Transcribed Image Text:Q1. 1) The data set "Boston" contains medv (median value of owner-occupied homes in $1000s) and 1stat (lower status of the population (percent)) in n-506 different census tracts in Boston. We wish to predict a value of medv using 1stat as a covariate. Use the R code to load the data set and create a plot of 1stat and medv. 11brary (ISLR2) head (Boston) ## crim zn indus chas ## 1 0.00632 18 2.31 ## 2 0.02731 07.07 # # 3 0.02729 0 7.07 # # 4 0.03237 0 2.18 # # 5 0.06905 0 2.18 # # 6 0.02985 0 2.18 nox rm age 0 0.538 6.575 65.2 4.0900 0 0.469 6.421 78.9 4.9671 0 0.469 7.185 61.1 4.9671 0 0.458 6.998 45.8 6.0622 0 0.458 7.147 54.2 6.0622 0 0.458 6.430 58.7 6.0622 2) Szz, Syy, Sry are defined by 71 ST1 = (T-F)², Syy-i-)², Szy=(Ti-T) (Vi-T). i=1 i=1 9.14 21.6 dis rad tax ptratio 1stat medv 1 296 15.3 4.98 24.0 2 242 17.8 2 242 17.8 3 222 18.7 2.94 33.4 3 222 18.7 5.33 36.2 3 222 18.7 5.21 28.7 4.03 34.7 = The least square estimate of a and 3 are i=1 Use the definition and using R, calculate Sr. Syy, Szy- 3) 1 The equation of the linear regression is y = a + Br+e. 3= Szy and & = 7-8. SII Use the formula given above and calculate the least square estimate of a and 3 (in R). The predicted value of y are calculate by the formula 91 = a + 3x₂ where à and 3 are the least square estimate of a and 3. Use the formula and calculate the predicted values ; (in R). Print the first 5 predicted values. The residual sum of squares (RSS) is defined by n Rss = Σ(m - 0;). i=1 Use the definition, and compute the RSS in R. Then compute RSS RSE = Vn-
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