Homework 9 Solutions

# Homework 9 Solutions - HW 9 SOLUTIONS Regression and...

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HW 9 SOLUTIONS Regression and Correlation 1. 12.41. The three residual plots, (i), (ii), and (iii), were generated after fitting regression lines to the three scatterplots, (a), (b), and (c). Which residual plot goes with which scatterplot? How do you know? Correct: Scatterplot (b) shows curvature, so it goes with residual plot (ii). In scatterplot (a), the points fan out as X increases, so this scatterplot goes with residual plot (iii). Finally, there are no unusual features in scatterplot (c), which goes with residual plot (i). 2. 12.5(modified). Twenty plots, each 10 x 4 meters were randomly chosen in a large field of corn. For each plot, the plant density (number of plants in the plot) and the mean cob weight (g of grain per cob) were observed. The results are given in the table. Plant Density X Cob Weight Y Plant Density X Cob Weight Y 137 212 173 194 107 241 124 241 132 215 157 196 135 225 184 193 115 250 112 224 103 241 80 257 102 237 165 200 65 282 160 190 149 206 157 208 85 246 119 224 a. Calculate the linear regression of Y on X . Correct: TI-84 After entering x’s in L1 and y’s in L2->STAT->TESTS and LinRegTTest->ENTER->Xlist: L1 Ylist: L2 Calculate->ENTER yields Y = 316.376 – 0.7206X b. Calculate s Y and specify the units. TI-84 STAT->CALC->ENTER->L2->ENTER yields s = 24.954 g c. Calculate the value of s Y|X and specify the units. Correct: TI-84 From LinRegTTest output we find S Y|X = 8.619254138 = 8.619 g

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d. Interpret the value of s Y|X in the context of this setting. Correct: Predictions of cob weight based on the regression model tend to be off by 8.6 g, on average. e. Calculate the value of r 2 Correct: TI-84 From LinRegTTest output, we find r 2 = 0.887 f. Interpret the value of r 2 in the context of the setting. Correct: 88.7% of the variability in grams of grain per cob is explained by variability in the number of plants per plot g. Now, using the QQplot of the residuals and a residual vs. predicted (fitted) values plot. Use these plots to comment on the assumptions (that can be checked here). Correct:
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Homework 9 Solutions - HW 9 SOLUTIONS Regression and...

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