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Question 4 5 points Save Answer Researchers wondered whether the size of a person's brain was related to the individual's mental capacity They selected a sample of right-handed Anglo introdu psychology students who had Scholastic Aptitude Test scores higher than 1350. The subjects were administered the Wechsler Adult Intelligence Scale-Revised to obtain their IQ scores. The MRI scans, performed at the same facility, consisted of 18 horizontal MR images. The comp of the 18 images, and the total count (in thousands) served as an index for brain size. The resulting data are presented in the following table uter counted all pixels with nonzero gray scale in IQ Score 133 137 138 132 Gender Female Female Female Female Female Female Female Female Female Female Male Male Male Male Male Male Male Male Male Male MRI Count 816.932 951.545 991.305 833.868 856.472 852.244 790.619 866.662 857.782 948.066 949.395 1001.121 1038.437 965.353 955.466 1079.549 924.059 955.003 935.494 949.589 132 135 130 133 133 140 140 139 133 133 141 135 139 141 144 given data, treating IQ score as the response (y) variable, and gender (1) and MRI count (x2) as predictors. Enter the given data in three columns in Minitab Express, then go to STATISTICS-> Regression-> Multiple Regression. Input the response variable, the one continuous predictor (MRI count), and the one categorical predictor (Gender) into the appropriate boxes in the Data tab. No other options need to be adjusted (but feel free to produce and examine residual plots from the Graphs tab, if you're curious about model conditions). Use this output to answer the Report your answers exactly as they appear in Minitab Express- do not round The Model: Based on the given data, the estimated regression model is X1 + X2 Note that Minitab Express internally converts the categorical predictor to an indicator variable which takes the value 0 for females and the value 1 for males (based alphabetical order of the levels of this predictor), Because of this, we can separate the above model into a separate regression line for each gender Based on the given data: the estimated regression equation for females is X2 whille the estimated regression equation for males is X2 Consider the hypotheses: Ha: Bi 0 With a P-value of we reject/fail to reject) Ho. The data does/ does not) provide significant evidence that this model is useful in predicting IQ score. Question 4 of 7 Moving to another question will save this response. Refer to the Brain Size data given in Question 4, and the resulting Minitab Express output. Report your answers exactly as they appear in Minitalb Express do not round. Gender Consider the hypotheses: Ho: B1 0 With a P-value of , the given data does/ does not) provide significant evidence that the IQ scores of males and females differ, with all else held constant. MRI Count: Consider the hypotheses: H0: β2-0 With a P-value of MRI count (is / is not) a significant predictor of IQ score.

Answer 1

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Minitab- Untitled-ISession] ols WindowHe Analysis of Variance Source Regression 2 106.28 53.14 4.74 0.023 DF Adj SS Adj MS F-Value P-Value MRI Count 1 18.08 18.08 1.61 0.221 | Gender 1 17.05 17.05 1.52 0.234 Error Total 17 190.52 11.21 19 296.80 Model Summary S R-sq R-sq (adj) R-sq (pred) 16.67% 3.34772 35.81% 28.26% Coefficients Coef SE Coef T-Value P-Value VIF Term Constant 119.1 MRI Count 0.0173 0.0137 1.27 0.221 1.81 Gender 0.000 12.09.91 2.49 2.02 1.23 0.234 1.81 Male Regression Equation Gender Female IQ Score 119.1 + 0.0173 MRI Count IQ Score 121.6 + 0.0173 MRI Count Hale Residuals vs Fits for IQ Score Current Worksheet: Worksheet1 O Type here to search