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Answer the following questions. You may use R on your own computer. 1) [ State the assumption of ANOVA. Then using the boxplot given above, comment the assump- tions of ANOVA are satisfied or not. 2) [ Describe how dummy variables regionSouth, regionWest (in output from summary() fune- tion) are used to indicate cach class. | Write down the estimated regression equation for each group separately. Give interpretation of these equations. Compute the values of these equations. 4) [ We wish to test of hypothesis V8 Ho: 141 142 143

Answer the following questions. You may use R on your own computer. 1) [ State the assumption of ANOVA. Then using the boxplot given above, comment the assump- tions of ANOVA are satisfied or not. 2) [ Describe how dummy variables regionSouth, regionWest (in output from summary() fune- tion) are used to indicate cach class. | Write down the estimated regression equation for each group separately. Give interpretation of these equations. Compute the values of these equations. 4) [ We wish to test of hypothesis V8 Ho: 141 142 143

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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balance 2000 1500 1000 C. d. 500 5) 0 South region Answer the following questions. You may use R on your own computer. 1) [ State the assumption of ANOVA. Then using the boxplot given above, comment the assump- tions of ANOVA are satisfied or not. T 2) [ Describe how dummy variables regionSouth, regionWest (in output from summary() fune- tion) are used to indicate each class. VS a. [ b. T 3) | Write down the estimated regression equation for each group separately. Give interpretation of these equations. Compute the values of these equations. 4) I We wish to test of hypothesis East 1 Use the significance level a=0.01. Ho: ₁1₂=143 H₁ : Not all group means are the same. Find the value of the test statistic and its distribution. Find the rejection region. Find the p-value of the test. Make a conclusion. We wish to test of hypothesis West Ho: 41 = 42 V8 Hy : μη # 12. Use the significance level a = 0.01. a. [ b. [ c. I d. [ ¹ Find the value of the test statistic and distribution of the test statistic. Find the p-value of the test or rejection region. Find the 99% confidence interval of the difference 2-11. Make a conclusion.
Transcribed Image Text:balance 2000 1500 1000 C. d. 500 5) 0 South region Answer the following questions. You may use R on your own computer. 1) [ State the assumption of ANOVA. Then using the boxplot given above, comment the assump- tions of ANOVA are satisfied or not. T 2) [ Describe how dummy variables regionSouth, regionWest (in output from summary() fune- tion) are used to indicate each class. VS a. [ b. T 3) | Write down the estimated regression equation for each group separately. Give interpretation of these equations. Compute the values of these equations. 4) I We wish to test of hypothesis East 1 Use the significance level a=0.01. Ho: ₁1₂=143 H₁ : Not all group means are the same. Find the value of the test statistic and its distribution. Find the rejection region. Find the p-value of the test. Make a conclusion. We wish to test of hypothesis West Ho: 41 = 42 V8 Hy : μη # 12. Use the significance level a = 0.01. a. [ b. [ c. I d. [ ¹ Find the value of the test statistic and distribution of the test statistic. Find the p-value of the test or rejection region. Find the 99% confidence interval of the difference 2-11. Make a conclusion.
Q2. We wish to compare Balance in 3 different Region. • Region: A factor with levels East, South, and West indicating the individual's geographical location. • Balance: Average credit card balance in 8. The mean balance for East, South and West are denoted, respectively, by #1, #2 and a. Data set The following code create the data set called dat that including balance and balance as variables. library (ISLR2) head (Credit) # Income Linit Rating Cards Age Education Own Student Married Region Balance #1 14.891 3606 283 2 34 11 No Yes South 15 Yes Yes West 3 82 4 71 11 No No West ## 2 106.025 6645 483 #3 104.593 7075 514 ## 4 148.924 9504 681 #5 55.882 4897 357 ##6 80.180 8047 569 3 36 11 Yes No West 16 No 10 No balance < Credit$Balance region <- as.factor (Credit$Region) dat < data.frame (region, balance) str(dat) 2 68 4 77 # region ## East: 99 # South: 199 # West :102 # # No Yes No No ## 'data.frame': 400 obs. of 2 variables: # $ region: Factor v/ 3 levels "East", "South",..: 2 3 3 3 2 2 1 321... ## $ balance: num 333 903 580 964 331... sunnary (dat) balance Min.: 0.00 1st Qu.: 68.75 Median 459.50 Mean : 520.01 3rd Qu.: 863.00 Max. :1999.00 No No Yes South No South 333 903 580 964 331 1151 Regression model The regression equation for ANOVA is given by y = Bo +31 + region South + B regionWest + E where ~ N(0,²). The dummy variables regionSouth and regionWest are created by the In() function and appear in the output below. Fitting the ANOVA model and output from sunmary() and anova () functions The following R code fit the ANOVA model with 1n() function and print outputs from summary() function and anova () function. anov_out <- In (balance region, data = dat) summary (anov_out) ## ## Call: # In (formula = balance region, data = dat) # Residuals: 10 Median ## Min 3Q Max ## -531.00 -457.08 -63.25 339.25 1480.50 ** ## Coefficients: # Estimate Std. Error t value Pr(>ltl) 46.32 11.464 56.68 -0.221 65.02 -0.287 # (Intercept) 531.00 #regionSouth -12.50 #regionWest -18.69 ** Signif. codes: 00.001 0.01 0.05 0.11 ## #Residual standard error: 460.9 on 397 degrees of freedom ## Multiple R-squared: 0.0002188, Adjusted R-squared: -0.004818 # F-statistic: 0.04344 on 2 and 397 DF, p-value: 0.9575 anova (anov_out) ## Analysis of Variance Table # #Response: balance <2e-16 *** 0.826 0.774 ## ## region ##Residuals 397 84321458 212397 Box plot Df Sun Sq Mean Sq F value Pr(>F) 2 18454 9227 0.0434 0.9575 boxplot (balance region, data dat) -
Transcribed Image Text:Q2. We wish to compare Balance in 3 different Region. • Region: A factor with levels East, South, and West indicating the individual's geographical location. • Balance: Average credit card balance in 8. The mean balance for East, South and West are denoted, respectively, by #1, #2 and a. Data set The following code create the data set called dat that including balance and balance as variables. library (ISLR2) head (Credit) # Income Linit Rating Cards Age Education Own Student Married Region Balance #1 14.891 3606 283 2 34 11 No Yes South 15 Yes Yes West 3 82 4 71 11 No No West ## 2 106.025 6645 483 #3 104.593 7075 514 ## 4 148.924 9504 681 #5 55.882 4897 357 ##6 80.180 8047 569 3 36 11 Yes No West 16 No 10 No balance < Credit$Balance region <- as.factor (Credit$Region) dat < data.frame (region, balance) str(dat) 2 68 4 77 # region ## East: 99 # South: 199 # West :102 # # No Yes No No ## 'data.frame': 400 obs. of 2 variables: # $ region: Factor v/ 3 levels "East", "South",..: 2 3 3 3 2 2 1 321... ## $ balance: num 333 903 580 964 331... sunnary (dat) balance Min.: 0.00 1st Qu.: 68.75 Median 459.50 Mean : 520.01 3rd Qu.: 863.00 Max. :1999.00 No No Yes South No South 333 903 580 964 331 1151 Regression model The regression equation for ANOVA is given by y = Bo +31 + region South + B regionWest + E where ~ N(0,²). The dummy variables regionSouth and regionWest are created by the In() function and appear in the output below. Fitting the ANOVA model and output from sunmary() and anova () functions The following R code fit the ANOVA model with 1n() function and print outputs from summary() function and anova () function. anov_out <- In (balance region, data = dat) summary (anov_out) ## ## Call: # In (formula = balance region, data = dat) # Residuals: 10 Median ## Min 3Q Max ## -531.00 -457.08 -63.25 339.25 1480.50 ** ## Coefficients: # Estimate Std. Error t value Pr(>ltl) 46.32 11.464 56.68 -0.221 65.02 -0.287 # (Intercept) 531.00 #regionSouth -12.50 #regionWest -18.69 ** Signif. codes: 00.001 0.01 0.05 0.11 ## #Residual standard error: 460.9 on 397 degrees of freedom ## Multiple R-squared: 0.0002188, Adjusted R-squared: -0.004818 # F-statistic: 0.04344 on 2 and 397 DF, p-value: 0.9575 anova (anov_out) ## Analysis of Variance Table # #Response: balance <2e-16 *** 0.826 0.774 ## ## region ##Residuals 397 84321458 212397 Box plot Df Sun Sq Mean Sq F value Pr(>F) 2 18454 9227 0.0434 0.9575 boxplot (balance region, data dat) -
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