A)

We were intrested to see if the physical activity is related to body mass index (BMI) of undergraduates. To test for this relationship, we considered a sample of 100 undergraduates and recorded their BMI and the average number of steps taken per day. Then we fitted a simple linear regression to our data. One particular undergraduate student, let's call her Ash, has a BMI of 34.3. Our model predicted Ash would have a BMI of 33.7. What is the residual of Ash's BMI?A group of scientists studied the relationship between the length of the body of a bullfrog and how far it can jump. They have fit a linear regression to predict the maximum jump (cm) based on the length (mm) of fifty randomly selected bullfrogs. Based on the model output below, what would be the predicted maximum jump (cm) to 3 decimal places for a bullfrog who is 147mm long? ## ## Call : ## 1m(formula = Jump - Length, data = df) ## ## Residuals: Min Median 3Q Max ## -2.47126 -0.59535 -0.01381 0.57285 2. 89200 ## Coefficients: # # Estimate Std. Error t value Pr(>Itl) ## (Intercept) 44.33372 12.90238 3.436 0.00123 ** ## Length 0.23068 0. 08668 2.661 0. 01056 ## - - ## Signif. codes: ## 0 '*** ' 0. 001 '** ' 0.01 '* ' 0. 05 '. ' 0.1 ' ': ## Residual standard error: 1.141 on 48 degrees of freedom ## Multiple R-squared: 0.1286, Adjusted R-squared: 0.1104 ## F-statistic: 7.082 on 1 and 48 DF, p-value: 0.01056 O 33.91 O 6517.288 O 44.334 78.244 O 0.231Given the R output below, what is the 95% confidence interval for /1, in this case? you may assume that the critical value, * =1.96 ? ## ## Call: ## lm(formula = y ~ x, data = df) ## Residuals: Min 10 Median 3Q Max ## -2. 30643 -0.70458 -0.07427 0. 61861 2. 88355 ## ## Coefficients: Estimate Std. Error t value Pr(>Itl) ## (Intercept) 3. 83803 1. 18545 3.238 0.00165 ** ## X 3. 00995 0. 04765 63.169