shared via CourseHero com This study resource was This study source was downloaded by 100000835462848 from CourseHero com on 10 29 2021 08 06 42 GMT 05 00 https www coursehero com file 6961803 Lectures11and12AdditionalPracticeSolutions Lectures 11 and 12 Additional Practice Solution 1 A corporation administers an aptitude test to all new sales representatives Management is interested in the extent to which this test is able to predict their eventual success The accompanying table records average weekly sales in ten thousands of dollars and aptitude test scores for a random sample of five representatives Use a 5 significance level wherever appropriate Test Score x Weekly Sales y xxi 2 xxi yyi 2 yyi yyxxii 4 1 1 1 3 9 3 6 5 1 1 1 1 1 5 4 0 0 0 0 0 6 7 1 1 3 9 3 4 3 1 1 1 1 1 25 20 0 4 0 20 8 5525 x 4520 y 1441 22 nxxSix 54201 22 nyySiy a Calculate the covariance between test score and weekly sales and the correlation between test score and weekly sales Cov X Y Sxy 2481 nyyxxii b Using the least squares method find the simple linear regression equation to predict weekly sales from test score 1221 xxyssb xbyb10 4 2 5 6 ScoresSale00 200 6 c Interpret the regression coefficients The sample slope tells us that for each additional point attained on the test average weekly sales are estimated to increase 20 000 The sample intercept tells us that when the test score is 0 average weekly sales are estimated to be 60000 This is an extrapolation shared via CourseHero com This study resource was This study source was downloaded by 100000835462848 from CourseHero com on 10 29 2021 08 06 42 GMT 05 00 https www coursehero com file 6961803 Lectures11and12AdditionalPracticeSolutions d Find the coefficient of determination and explain its meaning 80 020162 SSTSSRR 22 1 yisnyySST 4 5 20 221221 1 xisnbxxbSSR 2 2 4 1 16 We can explain 80 of the differences in weekly sales by relating it to the test score e Find the residuals from the regression Test Score x Weekly Sales y xy00 200 6 yyeii 4 1 2 1 2 1 6 5 6 5 6 1 5 4 4 4 4 0 6 7 6 7 6 1 4 3 2 3 2 1 f Find a point estimate of 15470 1333 1 MSES SSE SST SSR 20 16 4 Or SSE 4 1 1 0 1 1 222222ie 341 pnSSEMSE g What are the required data conditions for the inference procedures we discussed to be reliable i iid N 0 The error terms are independent at identically distributed according to the Normal distribution with a mean of 0 and some constant standard deviation h Find a 95 confidence interval estimate of the population slope Interpret it 5774 0 182 32 1121 bknStb 0 16 3 84 5774 04333 1 1 221 xibsnMSExxMSES shared via CourseHero com This study resource was This study source was downloaded by 100000835462848 from CourseHero com on 10 29 2021 08 06 42 GMT 05 00 https www coursehero com file 6961803 Lectures11and12AdditionalPracticeSolutions tc t0 025 3 3 182 We can be 95 confident that each additional point earned on the test is associated with between 1600 and 38 400 additional weekly sales on average i What are the hypotheses for the test to determine if test score is a significant predictor of weekly sales H0 1 0 Ha 1 0 j Find the F test statistic and the F critical point s for the test described in question i What is your conclusion C4C5Scatterplot of C5 vs C4Reject H0Do Not Reject H0 k Find the t test statistic and the t critical point s for the test described in question i What is your conclusion l Find 95 confidence interval for E y at x 5 12 Stykn 4 5 26 y 4 55 51333 1182 342 2 36 5 64 10 000 tRejectReject 2 2Reject H0 Do Not Reject H0 Fc 10 128 0 05 Fobs 1234116 MSEMSR Since Fobs Fc Reject H0 and conclude that using the linear model that relates weekly sales to test score provides significantly more explanation of the variation is weekly sales than y bar does 3 182 3 182 tobs 464 35774 002111 bsb Since tobs 3 182 Reject H0 and conclude that using the linear model that relates weekly sales to test score provides significantly more explanation of the variation is weekly sales than y bar does shared via CourseHero com This study resource was This study source was downloaded by 100000835462848 from CourseHero com on 10 29 2021 08 06 42 GMT 05 00 https www coursehero com file 6961803 Lectures11and12AdditionalPracticeSolutions m Find 95 prediction interval for y at x 5 yknSty 12 4 55 511333 1182 342 0 025 8 025 10 000 n Should the model be used to predict y when x 10 Explain No the sample data includes values for X in the range 4 6 Predicting Y when X 10 would be an extrapolation 2 The Pearson coefficient of correlation r equals 1 when there is no a explained variation b unexplained variation The unexplained variation is based on the residuals The relationship is deterministic all points fall on a straight line when r 1 so all residuals will be 0 c y intercept in the model d outliers 3 In a regression problem if the coefficient of determination is 0 95 this means that a 95 of the y values are positive b 95 of the variation in y can be explained by the variation in x c 95 of the x values are equal d 95 of the variation in x can be explained by the variation in y 4 In simple linear regression which of the following statements indicate no linear relationship between the variables x and y a Coefficient of determination is 1 0 b Coefficient of correlation is 0 0 c Sum of squares for error is 0 0 d Sum of squares for regression is relatively large 5 A scatter diagram includes the following data points x 3 2 5 4 5 y 8 6 12 10 14 Two regression models are proposed 1 y 1 2 2 5x and 2 y 3 2 0x Using the least squares method which of these regression models provides the better fit to the data Why The better equation is 1 It is the one that results in the lower SSE Find the residuals using both equations square them sum the squared residuals shared via CourseHero com This study resource was This study source was downloaded by 100000835462848 from CourseHero com on 10 29 2021 08 06 42 GMT 05 00 https www coursehero com file 6961803 Lectures11and12AdditionalPracticeSolutions 6 A simple linear regression between X and Y using 25 observations has SSR 100 The sample variance for Y is 6 25 Construct the Regression ANOVA table Source of Variation SS df MS F Regression 100 p 1 100 46 Error 50 n p 1 23 2 1739 Total 150 n 1 24 150 …