Are a person\'s brain size and body size predictive of his or her intelligence?
ID: 3323080 • Letter: A
Question
Are a person's brain size and body size predictive of his or her intelligence?
Response (y): Performance IQ scores (PIQ) from the revised Wechsler Adult Intelligence Scale. This variable served as the investigator's measure of the individual's intelligence.
Potential predictor (x1): Brain size based on the count obtained from MRI scans (given as count/10,000).
Potential predictor (x2): Height in inches.
Potential predictor (x3): Weight in pounds.
A sample of n = 38 college students:
PIQ Brain Height Weight
124 81.69 64.5 118
150 103.84 73.3 143
128 96.54 68.8 172
134 95.15 65.0 147
110 92.88 69.0 146
131 99.13 64.5 138
98 85.43 66.0 175
84 90.49 66.3 134
147 95.55 68.8 172
124 83.39 64.5 118
128 107.95 70.0 151
124 92.41 69.0 155
147 85.65 70.5 155
90 87.89 66.0 146
96 86.54 68.0 135
120 85.22 68.5 127
102 94.51 73.5 178
84 80.80 66.3 136
86 88.91 70.0 180
84 90.59 76.5 186
134 79.06 62.0 122
128 95.50 68.0 132
102 83.18 63.0 114
131 93.55 72.0 171
84 79.86 68.0 140
110 106.25 77.0 187
72 79.35 63.0 106
124 86.67 66.5 159
132 85.78 62.5 127
137 94.96 67.0 191
110 99.79 75.5 192
86 88.00 69.0 181
81 83.43 66.5 143
128 94.81 66.5 153
124 94.94 70.5 144
94 89.40 64.5 139
74 93.00 74.0 148
89 93.59 75.5 179
Run the regression in Excel and copy/paste the output here.
(15 pts)
a) Evaluate the model using the R2 value.
b) Form the model.
c) Based on ANOVA table in the outputs, what can you say about the three variable used to build the model? Which variables can be used for predicting PIQ? Why?
Explanation / Answer
following information has been generated
(a) R2=0.2949, it is in low range, so model is not good fit
(b)PIQ=111.3536+2.0604*Brain-2.7319*Height+0.0006*Weight
(c) based on ANOVA, model is good fit as p-value of the F of the regression is significanct at significance level alpha-0.05
since at alpha=0.05 , Brain & Height are significant and weight is not significance. so Brain and height can be used to predict PIQ
SUMMARY OUTPUT Regression Statistics Multiple R 0.54308306 R Square 0.29493921 Adjusted R Square 0.232727964 Standard Error 19.79439032 Observations 38 ANOVA df SS MS F Significance F Regression 3 5572.744435 1857.581 4.740930761 0.00721527 Residual 34 13321.8082 391.8179 Total 37 18894.55263 Coefficients Standard Error t Stat P-value Intercept 111.3536083 62.97109646 1.768329 0.085978536 Brain 2.060366798 0.563446825 3.656719 0.000855632 Height -2.731929162 1.229428631 -2.22211 0.033033818 Weight 0.000559937 0.197066131 0.002841 0.997749527Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.