Please do the following questions with R code balance200015001000C.d.5005)0SouthregionAnswer 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.T2) [Describe how dummy variables regionSouth, regionWest (in output from summary() fune-tion) are used to indicate each class.VSa. [b.T3) |Write down the estimated regression equation for each group separately. Give interpretationof these equations. Compute the values of these equations.4) IWe wish to test of hypothesisEast1Use the significance level a=0.01.Ho: ₁1₂=143H₁ : 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 hypothesisWestHo: 41 = 42 V8 Hy : μη # 12.Use the significance level a = 0.01.a. [b. [c. Id. [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 setThe 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 3411 NoYes South15 YesYes West3 824 7111 NoNo 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 5693 3611 YesNo West16 No10 Nobalance

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Please do the following questions with R code balance200015001000C.d.5005)0SouthregionAnswer 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.T2) [Describe how dummy variables regionSouth, regionWest (in output from summary() fune-tion) are used to indicate each class.VSa. [b.T3) |Write down the estimated regression equation for each group separately. Give interpretationof these equations. Compute the values of these equations.4) IWe wish to test of hypothesisEast1Use the significance level a=0.01.Ho: ₁1₂=143H₁ : 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 hypothesisWestHo: 41 = 42 V8 Hy : μη # 12.Use the significance level a = 0.01.a. [b. [c. Id. [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 setThe 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 3411 NoYes South15 YesYes West3 824 7111 NoNo 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 5693 3611 YesNo West16 No10 Nobalance < Credit$Balanceregion <- as.factor (Credit$Region)dat < data.frame (region, balance)str(dat)2 684 77#region## East: 99# South: 199# West :102##NoYesNoNo## '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)balanceMin.: 0.001st Qu.: 68.75Median 459.50Mean : 520.013rd Qu.: 863.00Max. :1999.00NoNoYes SouthNo South3339035809643311151Regression modelThe regression equation for ANOVA is given byy = Bo +31 + region South + B regionWest + Ewhere ~ N(0,²). The dummy variables regionSouth and regionWest are created by the In() functionand appear in the output below.Fitting the ANOVA model and output from sunmary() and anova () functionsThe following R code fit the ANOVA model with 1n() function and print outputs from summary() functionand anova () function.anov_out <- In (balance region, data = dat)summary (anov_out)#### Call:# In (formula = balance region, data = dat)# Residuals:10 Median## Min3Q Max## -531.00 -457.08 -63.25 339.25 1480.50**## Coefficients:#Estimate Std. Error t value Pr(>ltl)46.32 11.46456.68 -0.22165.02 -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: 0.9575anova (anov_out)## Analysis of Variance Table##Response: balance<2e-16 ***0.8260.774#### region##Residuals 397 84321458 212397Box plotDf Sun Sq Mean Sq F value Pr(>F)2 18454 9227 0.0434 0.9575boxplot (balance region, data dat)-

Accepted Answer

In the given model, the dependent variable is average credit card balance which is studied using an…