Question

Wide po is the intercept of the population regression line , is the slope of the population regression line s the error form, and the subscriptions over observations, ist.. For this, you collect data from a random sample of 250 people. After analyzing the data, you determine that the covariance between people's weight and the number of times they eat out in a month is 4.62 and the variance of the number of times people eat out in a month is 3.78. You also find that the mean weight of people in the sample is 63.82 kg and the mean number of times people at out in a month is 2.25 The OLS estimator of the slopes, is 122 (Round your answer to two decimal places.) The OLS estimator of the intercept fois 61.08 (Round your answer to two decimal places) Which of the following statements are true in describing the estimates of the coefficients of the regression in (Check all that apply) A The slopes is the percentage change in weight due to a unit change in the number of times a persones out in a month B. The intercept shows the predicted weight when an individual does not go out to eat. The value of the intercept therefore has no real world meaning in this case. C. The slope, P. Is the change in weight due to a unit change in the number of times a personals out in a month D. The intercept shows the predicted weight when an individual does not go out to eat. The value of the root has real world meaning in this case

Answer 1

OLS estimator $\beta$ ₁ = Cov (X, Y) / Var(X) = 4.62/ 3.78 = 1.22

OLS estimator $\beta$ 0 = $\overline{Y}$ -  $\beta$₁$\overline{X}$ = 63.82 - 1.22 * 2.25 = 63.82 - 2.75 = 61.08

The slope, $\beta$ ₁ shows the change in Y due to unit change in X. So, here it shows the change in weight due to a unit change in the number of times a person eats out in a month. The vertical intercept, depicted by $\beta$ 0 shows the value of Y if X is zero. In this case, it shows the predicted weight when an individual does not go out to eat. So, it has a real world meaning in this case.

Hence, option C and D are correct.