The regression equation is: lifespan = 3.75 - 2.15 weight Predictor Coef St Dev t ratio $p$ Constant 3.749 0.861 2.51 0.000 Weight -2.151 0.823 -1.30 0.000 s = 0.3138 R-sq = 96.2% R-sq (adj) = 96.1%
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Ivan K.
In a certain species of bug, lifespan (in days) is related to body weight (in grams) by the regression equation: Lifespan = 481 - 0.06Weight The equation was produced using a random sample of 44 bugs. a) Which of the following best describes the slope of the regression line? 1.Lifespan in days decreases by 0.06, on average, for every 1 gram increase in the bug's weight. 2.Lifespan in days increases by 0.06, on average, for every 1 gram increase in the bug's weight. 3.The weight of a bug increases by 0.06, on average, for every 1 day increase in that bug's lifespan. 4.Approximately 0.06% of the variability in a bug's lifespan is explained by its linear relationship with the weight of that bug. 5. The weight of a bug decreases by 0.06, on average, for every 1 day increase in the bug's lifespan. b) Which of the following gives the most sensible interpretation of the intercept of the regression line? 1. When a bug weighs 0.06 grams, we expect it to live 481 days on average. 2.For every 1 gram increase in a bug's weight, we predict its lifespan should change by -0.06 days on average. 3.When lifespan equals 0, we predict a bug should weigh 481 grams. 4. The relationship between lifespan and weight is 481% stronger when lifespan equals 0 than when it equals -0.06. 5. Since bugs cannot have a weight of 0 grams, there is not a good sensible interpretation in this context. c) What is the residual for a bug that weighs 1 gram and lived for 458 days? (3 decimal places)
Jacob F.
Scientists have long believed that linear regression could be used to predict the brain weight of nonhuman mammals from the body weight. In one study, body weight, in kilograms, and brain weight, in grams, of 22 nonhuman mammals were measured. A linear regression was performed yielding the output below. Reg Analysis: Brain Wt. vs Body Wt. n = 22 Predictor Coef SE Coef T P Constant 68.688 3.1270 21.966 0.004 Body Wt 1.096 0.1308 8.379 0.005 s = 103.995 R-sq = 77.8% R-sq (adj) = 77.6% Assuming that all conditions for inference are met, which of the following represents a 95% confidence interval for the slope of the least squares regression line? a. 1.096 ± 2.086(0.1308) b. 1.096 ± 2.086(103.995) c. 1.096 ± 2.086(0.1308 / √22) d. 1.096 ± 2.086(103.995 / √22) e. 68.688 ± 2.086(3.1270) 2. Refer to the situation described in problem #1 above. If we were to carry out a significance test for the slope of the true regression line, what test would we use and with how many degrees of freedom? a. t-test for linear regression with df = 20 b. t-test for linear regression with df = 21 c. t-test for linear regression with df = 22 d. t-test for linear regression with df = 24 e. z-test for linear regression with no need to use degrees of freedom
Shyam P.
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