Question

Gender Selfconce ID GPA 7.940111 8.292107 4.643 100 7.470107 67 2 4 3 52 8.882 114 7.585 115 7.650111 58 71 51 2.412 97 6.000 100 8.833 112 4 9 51 7.470 104 35 5.528 89 54 13 7.167104 54 64 56 69 7.571 102 4.700 91 8.167114 15 17 7.822 114 65 7.598 103 4.000 106 19 40 6.231 105 21 7.643 113 1.760 109 20 24 6.419 108 56 68 69 9.648 113 2 27 10.700 130 28 10.580 128 70 9.429 128 8.000 118 9.585 113 29 30 80 53 31 65 32 9.571 120 67 8.998 132 62 34 8.333 111 39 35 8.175 124 8.000 127 9.333 128 71 59 36 37 60 64 38 39 9.500 136 9.167106 71 40 10.140 118 72 9.999119 54 10.760 123 64 9.763 124 58 70 45 9.410 126 46 9.167 116 72 2072667337140030 6 4 9 4 7 4 3 9 7 3 6 4 2800116 774546665 6 6 5 6 6 6 3 5 6 4 4 4 667536364267525 222212222221112222221212211212111212 20035 9007 1217, 6 0 1 2 0 1 3 2 1 0 2 9 1 1 1 0 4 0 1 0 1 0 0 780611130 133 525073 787786770355823255877537643580600778 64640364379, 9 3 8 5 6 7 3 8 4 3 2 3 6 9 1 3 892300553 131649165122983012562831978898905009 998333770677878588775779787473599666 678012345678901234589124678903456789 444, 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 Refer to the data file sevengr.txt, which contains data on GPA, IQ, Gender and Self-concept for 78 seventh grade students in a rural Midwestern school. 1. Use software to generate a scatterplot of self-concept versus IQ. Write a sentence interpreting the scatterplot. 2. Compute and state the correlation between self-concept and IQ and write a sentence interpreting the correlation 3. Compute and state the equation of the least-squares regression line for predicting self-concept based on IQ, and write a sentence interpreting the slope of the least-squares line. 3. Compute and state the equation of the least-squares regression line for predicting self-concept based on IQ, and write a sentence interpreting the slope of the least-squares line. 4. Give the square of the correlation between self-concept and IQ, and interpret. What does the value ofindicate about the usefulness of using the least-squares line in #3 to predict self-concept? 5. Obtain the residuals and graph a scatterplot of residuals versus IQ. Which observation has the largest residual? 6. Observation 22 (Self-concept 20, IQ 109) might be considered an outlier. Repeat #2 omitting observation 22. Explain the reason for the change in the correlation.

Answer 1

Ans. Let GPA GENDERx CONCEPTx The multiple regression model is given bv.

Use the "Excel" to calculate the regression coefficients SELECT>Data Data Analysis, see the screenshot given below. 17.940 111 4.643 10 Input 61 41 7.4 10 nput Y Range: 5$2:S8$80 7 58882 114 input x Range: 7.585 115 constat B Zero 7.650 111 Confidence Level: 9% 10 S2412 9 6.0001 100 11 9 Output optons 08.833 11 12 9 Qutput Range: 13 11 14 25.528 8 New Worksheet Bly: O New Workbook 7.1671 15 13 100 57110 Readual Pots neFtPlots 64 1614 sandardized Resdas 17 54700 91 Normal Probability Normal Probablity Plots 18 68.1 7.822 11 19 17 20 8 7 0 21 9401

2 obs GPA IQ GENDER CONCEPT SUMMARY OUTPUT 67 8.292 107 45 Regression Statistics 4.643 100 52 MultipleR 0.721683 6 7470 107 66R Square 0520826 58Adjusted RSc 0.5014 51 Standard Erro 1.482532 58.882 114 7.585 115 7.650 111 71 Observations 78 6.000 100 49 ANOVA 8.833 112 F ignificance F 12 1 MS 13 7.470 104 35 Regression 3 176.7822 58.92741 26.81077 7.633E-12 54 Residual 5.528 89 14 12 74 162.6447 2.197901 7.167 104 54 Total 15 13 77 339.4269 16 14 7.571 102 17 15700 91 Err tstat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 8.167 114 18 1 69 Intercept 5.02236 1.469531-3.41766 0.001037.9504648-2.0942546-7.9504648152.094254576 7.822 114 0.084117 0.014955 5.624762 3.13E-07 0.05431883 0.1139147 0.0543188330.113914711 19 1 20 18 9103 65 GENDER 0.968521 0.349484 2.771287 0.007057 0.27215845 1.6648836 0.27215845 1.664883609 106 40 CONCEPT 21 1 0.051293 0.015646 3.278228 0.001593 0.02011646 0.0824691 0.0201164570.082469097

O os13 (CoNCEPT Civen EDR 2