CONCORDIA UNIVERSITY



Bivariate RegressionSupplemental Problems1. Consider the following data set, with a correlation (r) of -0.74: Yx3446273583a) Find the regression constant (b0) and coefficient (b1).b) Fill out an ANOVA table and find the obtained F ratio? Is the model a good fit of the data?c) What is the R2?d) What is the power of the study?e) If the individual scores 9 on the predictor variable would be the predicted outcome value?f) If the predictor value decreases by 1 standard deviation, how much would you outcome variable to change?g) What is the standard error of the estimate?2. Consider the following data set with a correlation (r) of 0.68: Yx191036115226a) Find the regression constant (b0) and coefficient (b1).b) Fill out an ANOVA table and find the obtained F ratio? Is the model a good fit of the data?c) What is the R2?d) What is the power of the study?e) If the individual scores 8 on the predictor variable would be the predicted outcome value?f) If the predictor value increases by 2 standard deviations, how much would you outcome variable to change?g) What is the standard error for testing significance of the slope?h) Figure the confidence interval (95%).3. Suppose that there is a .45 correlation between IQ (M = 100, SD = 15) and verbal SAT score (M = 500, SD = 100). What verbal SAT score would you predict for someone who has an IQ of 90? a) 433 b) 470 c) 490 d) 510 4. Given that Mx = 57, SDx = 18.5, My = 44, SDy = 16, and that the slope of the regression line for predicting Y from X, b1, is -.52, what must the correlation between X and Y be?a) -.45 b) -.60 c) -.67 d) +.455. If the slope for predicting Y from X, b1, is 16 and the Y-intercept, b0, is 400, what prediction for Y corresponds to X = 20?a) 320 b) 420 c) 560 d) 720 6. Given the following regression equation: Y = 5+ 16X, for what value of X would 29 be predicted?a) 1.5 b) 1.8 c) 464 d) 469 7. Suppose that a regression equation for predicting a midterm score from the number of practice problems solved prior to the exam is as follows: Y' = 45+ .8X. What midterm score is predicted for someone who does not solve any practice problems?a) .8 b) 45 c) 56.25 d) 0 8. Given the following summary statistics: eq \O() Mx= 36, sx = 1.6, My= 44, sy = 2.8, r = .7, N = 10, what is the unbiased estimate for the standard error of the estimate?a) 1.21 b) 1.63 c) 2.0 d) 2.11 9. A researcher runs a bivariate regression models with 25 cases, and obtains the following values: SST = 1000; SSM = 632; SSR = 368. What value for the standard error of the estimate will he obtain? a) 4 b) 5.24 c) 16 d) 27.48 10. You are given the following information concerning a bivariate analysis: N = 12; SEest = 10; SSt = 1100. What is the obtained F score for the analysis? a) 1 b) 2 c) 5 d) 1011. You obtain the following values: SDX = 5; SSR = 500; N = 22; b1 = .655. What is the obtained t value when testing the significance of the slope? a) 2 b) 3 c) 4 d) 5 12. If the raw-score prediction for Y is always the same as the raw-score of X (the variable used to make the predictions), the slope of the regression line will be:a) zero b) +1.0 c) infinity d) it depends on the standard deviations of X and Y13. The Y-intercept is: a) the value of Y when X equals zerob) the value of Y when r equals zeroc) the value of Y when the slope equals zerod) the value of X when Y equals zero 14. Homoscedasticity exists in the population, when for every X value:a) the variance of the Y variable is the sameb) the variance around the regression line is the samec) the slope of the regression line is the samed) the Y-intercept is the same 15. Suppose that there is a .6 correlation between IQ (Mx = 100, sx = 15) and verbal SAT score (My = 500, sy = 100) for 20 pairs of scores. What would be the standard error of the estimate when predicting IQ from verbal SAT? a) 79.47 b) 81.53 c) 82.19 d) 84.21 16. A researcher conducted a bivariate regression in which the X and Y variables had a correlation of r = .6. There were 22 participants in her study. She obtained an F score of 11.25, and SStotal of 1000. Use this information to fill in the tables below.RR2Std. error of the EstimateSSDfMSFRegression11.25ResidualTotal1000ANSWERS1.a) Y = 9.5+-1.1*xb) YXMean of y(y – mean)(y-mean)2Model(y – model)(y – model)2(Model – Mean)(Model – Mean)2344-115.1-2.14.411.11.21464002.91.11.21-1.11.21274-241.80.20.04-2.24.84354-114-11008344166.21.83.242.24.84229.912.1SourceSSDfMSFModel12.1112.13.67Residual9.933.3No F obtained is less than F critical (1,3) = 10.13c) R2 = SSmodel/SStotal = 12.1/22 = .55d) .16 or 16%e) Y = 9.5+-1.1*(9) = -.4f) Standardized beta = -.742; Change of 1 SD in X = -.746 SD change in Y; Change in Y = XSD x Beta x YSD = -1 x -.746 x 2.35 = 1.75g) 2. a) Y = 1.02+.60*xb) YXMean of y(y – mean)(y-mean)2Model(y – model)(y – model)2(Model – Mean)(Model – Mean)291045256.912.094.372.918.47364-114.55-1.552.400.550.3114-391.6-0.60.36-2.45.76524112.192.817.90-1.813.28264-244.55-2.556.500.550.34021.5318.11SourceSSDfMSFModel18.11118.112.52Residual21.5337.17No F obtained is less than F critical (1,3) = 10.13c) R2 = SSmodel/SStotal = 18.11/39.64 = .46d) .13 or 13%e) Y = Y = 1.01+.59*(8) = 5.73f) Standardized beta = .68; Change of 1 SD in X = .68 SD change in Y; Change in Y = XSD x Beta x YSD = 2 x .68 x 3.16 = 4.30g) h) 3. b4. b5. d6. a7. b8. d9. a10. a11. b12. b 13. a14. b15. c16. RR2Std. error of the Estimate.6.365.66SSDfMSFRegression360136011.25Residual6402032Total1000 ................
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