Assignment on Statistics (Solved)
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Added on 2021-06-14
Assignment on Statistics (Solved)
Added on 2021-06-14
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STATISTICSASSIGNMENT[Pick the date]Student Name
Question 1The various descriptive assumptions with regards to simple linear regression are highlightedbelow.Homoscedasticity - This tends to imply that the variance associated with predictor valuesabout the regression line should be the same. If there is violation of the same in anysignificant manner, then it may be assumed that the significance of the slope coefficientdeclines and heteroscedasticity would be present (Lieberman, et. al., 2013).Normality – It is essential that the residuals must be normally distributed which impliesthat there should not be any particular pattern that is observed for the same. This isnormally verified through the residual plot and the positioning of the points therein. Question 2The various inferential assumptions with regards to simple linear regression are highlightedbelow (Hastie, Tibshirani & Friedman, 2011).Linearity – It is essential that for reliable slope estimation, the underlying relationshipbetween the variables should be linear which would lead to linear values of parametersand errors. The presence of non-linearity in the data leads to the slope being insignificant.No autocorrelation – This implies that the values of the independent variables must notexhibit significant correlation with each other. This is ascertained by checking whetherthe residuals are independent of each other or not. In case of residuals being dependent,then autocorrelation is present (Taylor & Cihon, 2004).No presence of outliers – it is imperative that the concerned data used for regressionanalysis should be free from outliers so as to ensure that the various coefficients of theregression line are not adversely impacted by the same. Also, in case of presence ofoutliers, it makes sense to ignore such observations (Koch, 2013).Question 3a)In the given case, the various relevant details related to simple regression are highlighted.Y or GPA of the public administration majors is the dependent variable while X or weeklyminutes of television. The regression equation between the two variables is provided asfollows.1
Y – 3.3 -0.0009XHere the slope or b = -0.0009The slope value highlights that an increase in weekly television viewing by 1 hour wouldtend to decrease the average GPA of a public administration major student by 0.0009. Intercept value or a = 3.3The intercept value implies that for a student with public administration majors who weeklyTV watching is zero would tend to score a GPA of 3.3.Also, the regression coefficient between the two variables is -0.53 which implies that theregression between the two variables is negative and medium in strength. Further, the factthat both r and b are significant at 5% significance level implies that we can state with 95%confidence that the relation between GPA and weekly minutes of television is statisticallysignificant (Flick, 2015).b)If r and b are not statistically significant at 5% level of significance, then we can concludewith 95% confidence that the inverse relationship between GPA and the weekly minutesspent watching television is not significant. However, there is a 5% risk that the relationbetween the given variables may be significant but still not captured in the hypothesis test.c)Additional information would be regarding the sample size and also about the range ofsamples that have been used for estimating the given regression model. The sample size isrequired so as to understand whether the sample size used for prediction of the modelseems large enough or not so as to be representative of the population of interest. This isimperative as a sample size smaller than the minimum sample size would lead to anunrepresentative sample and hence lead to biased results (Hastie, Tibshirani & Friedman,2011).Further, the range of sample variables is imperative since reliable estimates based onregression equation can be made only within the range of the sample variables that havebeen used for predicting the regression model in the first place. For instance, if in thegiven case, the weekly minutes of television viewing for the sample students highlighted arange of 150 to 250 minutes, then the regression model estimated above cannot be used toestimate the grade of a student with weekly television watching minutes as 300 minutes2
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