Is IQ related to GPA?If a student’s IQ is 117, what GPA would you predict?How much of the variation in GPA is explained by IQ?What can you conclude based upon the standard error of the estimate? Regression WorksheetThe following data are from a random sample of thirty cases from a study byHowell & Huessy (1981). The data represent the relationship between IQ scoreson the Otis-Lennon Mental Abilities Test, administered while subjects were infifth to eighth grade, and GPA in ninth grade.SubjectIQGPA11022.7521084.0031092.2541183.00791.67882.2571002.508.923.501313.7510832.75111154.0012922.2313953.0014902.50151062.7516852.7517952.7518972.6719932.0020812.0021113.0022951.50231063.752483.6725811.50261123.0027851.75281153.7529861.0030852.50

Name: Is IQ related to GPA?If a student’s IQ is 117, what GPA would you pred
Uploaded: 2024-03-20T07:06:16.000Z
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Description: Is IQ related to GPA?If a student’s IQ is 117, what GPA would you predict?How much of the variation in GPA is explained by IQ?What can you conclude based upon the standard error of the estimate? Regression WorksheetThe following data are from a rando

Given Info : The provided data are from a random sample of thirty cases from a study by Howell & Huessy (1981). The data represent the relationship between IQ scores on the Otis – Lennon Mental Abilities Test , administered while subjects were in fifth to eighth grade , and GPA in ninth grade . Use a scatter plot (XY chart) to show scientific XY data. Scatter plots are often used to find out if there's a relationship between variable X and Y. To find out if there is a relationship between X (IQ) and Y (GPA), execute the following steps : 1. Select the range A1:B10. 2. On the Insert tab, in the Charts group, click the Scatter symbol. 3. Click Scatter. Result: Interpretation : Points on plot are scattered and directed towards increasing order . Therefore , X and Y shows linear relationship between them . If your data shows a linear relationship between the X and Y variables, you will want to find the line that bestfits that relationship. That line is called a Regression Line and has the equation ŷ= a + b x. The Least Squares Regression Line is the line that makes the vertical distance from the data points to the regression line as small as possible. Here, IQ (X) is independent variable and GPA (Y) is dependent variable . The independent variable is XX, and the dependent variable is YY. In order to compute the regression coefficients, the following table needs to be used: X Y X*Y X2 Y2 102 2.75 280.5 10404 7.5625 108 4 432 11664 16 109 2.25 245.25 11881 5.0625 118 3 354 13924 9 79 1.67 131.93 6241 2.7889 88 2.25 198 7744 5.0625 100 2.5 250 10000 6.25 92 3.5 322 8464 12.25 131 3.75 491.25 17161 14.0625 83 2.75 228.25 6889 7.5625 115 4 460 13225 16 92 2.23 205.16 8464 4.9729 95 3 285 9025 9 90 2.5 225 8100 6.25 106 2.75 291.5 11236 7.5625 85 2.75 233.75 7225 7.5625 95 2.75 261.25 9025 7.5625 97 2.67 258.99 9409 7.1289 93 2 186 8649 4 81 2 162 6561 4 111 3 333 12321 9 95 1.5 142.5 9025 2.25 106 3.75 397.5 11236 14.0625 83 0.67 55.61 6889 0.4489 81 1.5 121.5 6561 2.25 112 3 336 12544 9 85 1.75 148.75 7225 3.0625 115 3.75 431.25 13225 14.0625 86 1 86 7396 1 85 2.5 212.5 7225 6.25 Sum = 2918 77.49 7766.44 288938 221.0271 Based on the above table, the following is calculated : Therefore, based on the above calculations, the regression coefficients (the slope mm, and the y-intercept nn) are obtained as follows: Therefore, we find that the regression equation is: If a student’s IQ is 117 i.e. X = 117 Y = - 1.7773 + 0.0448 * 117 Y = 3.4643 . If a student’s IQ is 117, then GPA would be predict = 3.4643 .