1.  Suppose you’ve planted 30

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1.  Suppose you’ve planted 30 tomato plants in your garden, 10 each of three different varieties (labeled A, B, C), and you want to compare the varieties in terms of the weight of their fruits.  However, you also want to consider the height of the plants.  So you weigh (in ounces) one ripe tomato from each plant, as well as the height of the plant (in meters).  Below are the results from a general linear model on your data: Table 1 – Regression Results Estimate St. Error t-statistic p-value Intercept 2.98 0.51 5.84 < 0.01 Var_A -0.78 0.21 -3.71 < 0.01 Var_B 0.41 0.26 1.58 0.13 Height 0.20 0.09 2.22 0.04 Here is how you dummy coded your categorical variable (variety of tomato plant): Variable Nameà Var_A Var_B Plant A 1 0 Plant B 0 1 Plant C 0 0 a.  Write your overall regression equation predicting fruit weight from tomato variety and height. (4 pts) Weight= 2.98 – 0.78(Var_A) + 0.41(Var_B) + 0.20(Height) b. Which assumption would you have failed if you had weighed two fruits from each plant?  (1pt) Two fruits from the same tree would violate independence because they would be affected by the same variables. c. Suppose a fruit from a variety A plant that was 0.9 m tall weighed 2.09 oz.  What is this tomato’s residual? (3pt) d. Which variety had the highest mean fruit weight, while controlling for height? (2pts

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