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# Consider the fitted regression line

December 6, 2021No Comments

Consider the fitted regression linescore=6.641-1.9STR+1.06 Income,R2=0.56,n=420,(0.014)(1.9)(1.00)ewhere score denotes the student’s percentage test score (i.e.score 60 means 60 percentagepoints),STR denotes the student to teacher ratio,Income denotes the average annual per capitaincome in the school area(measured in thousands of sterling pounds;Income 2 means E2000),R2 is the R-squared value or coefficient of determination,and n is the sample size.The values inbrackets underneath the parameter estimates are the corresponding standard errors.Use thisinformation to answer questions 2-5 below.2.What is the most appropriate interpretation of the estimate 1.9?(a)If the student to teacher ratio increase by one,the student’s test score expected to increaseby 1.9%,ceteris paribus.(b)If the student to teacher ratio increase by one,the student’s test score expected to decreaseby 1.9%,ceteris paribus.(c)If every teacher corresponds to one extra student,the student’s test score is expected to dropby 1.9 percentage point.(d)If the student to teacher ratio increase by one,the student’s test score expected to decreaseby 1.9 points,ceteris paribus.(e)If the student to teacher ratio increase by one,the student’s test score is expected to decreaseby 1.9 percentage points,when Income remains unchanged.3.Which of the following statements is the most appropriate?(a)This model is useless,as none of the explanatory variables (i.e.STR and Income)is statis-tically significant using t tests.(b)This model is useless,since the STR has an unexpected sign and a small t statistic.(c)This model is useful,simply because that R squared 0.56 means about 56%variation inscore being explained by the variation of this model.(d)The model is useful,because the specified relationship between variables makes sense andthe F statistic is large.←4.Compute the value of the test statistic for the overall significance of this regression.(a)1.00.(b)1.06.e(c)265.36.(d)474.36.5.If the student to teacher ratio increases by 1 point,and the average annual per capita income inthe school area increases by￡63，calculate the approximate change in the value of score.e(a)Decrease by 1.165.(b)Increase by 1.(c)Increase by 5.476.(d)Increase by 6.157.(e)Increase by 7.641.(f)Increase by 12.798.