The Child Health and Development Studies investigate a range of topics. One study considered all pregnancies between 1960 and 1967 among women in the Kaiser Foundation Health Plan in the San Francisco East Bay area. For each baby in the study, the baby's weight at birth in ounces (Birthweight) and the length of the pregnancy in days (Gestation) was recorded. The scatter plot and a summary of a subset of the data is given below. The correlation between Gestation and Birthweight was found to be r = 0.3642. Round all calculated answers to 4 decimal places. Baby Birthweight and Gestation 160 O 140 O O Birthweight In ounces 120 O O . I "I: . O {3015 a '9'. . I '.. . .0 O. ' I I 100 I I . I- I. I {:5- I .. O O 80 . 200 250 300 Gestation in days Birthweight 118.7851 17.6474 1. The relationship between Birthweight and Gestation is best described as ??? v and ??? v . 2. Calculate the slope and intercept for the linear regression that predicts Birthweight from Gestation. Note: Do not use rounded values for subsequent calculations! Slope: and Intercept: 3. What is the R2 for this study's regression of Birthweight from Gestation? 4. A different study into the linear relationship between baby gestation time and birthweight yielded an R2 value of 0.1129. Which of the following is a correct interpretation of their R2 value? 0 A. There is little evidence that the linear model is a good fit. 0 B. 0.1129% of the variation in Gestation can be explained by the linear relationship with Birthweight. O C. 11.29% of the variation in Birthweight can be explained by the linear relationship with Gestation. O D. 11.29% of the variation in Gestation can be explained by the linear relationship with Birthweight. 5. A baby in the data set had a gestation time of 282 days and an observed birthweight of 109 ounces. The model estimates the birthweight for this baby to be 120.202 ounces. Calculate the residual for this baby. Residual = Choose from the dropdown menus to correctly interpret the residual. The regression model ??? v the birthweight for this baby because the residual i5 ??? v 6. Below are a scatterplot of residuals by fitted values, and a histogram and Q-Q plot of the residuals. Residual Plot Histogram of residuals 0-0 plot of Residuals 60 l 40 50 40 20 ReSiduals Frequency 20 30 Residuals 420 10 l A L- l l l l l l l l l I so so 100 no 120 130 140 ~40 -20 0 20 40 50 >3 -2 -| 0 1 2 3 40 Fined Values Reslduals Theoretical Ouantiles Why do researchers look at these plots of the residuals? (check all that apply): [3A. To determine if the residuals are roughly normally distributed. C] B. To judge whether the variability of the data about the regression line is nearly constant. C] C. To investigate whether the data has an underlying structure or pattern, which may indicate the observations are not independent C] D. To make sure the residuals follow a linear trend. C] E. To measure the variability of the slope and intercept of the model. C] F. To explain the strength of the evidence of a linear relationship between the residuals and fitted values