Question

Suppose that you want to estimate the relationship between​ people's weight ​(W​) and the number of times they eat out in a month ​(EO​): Upper W Subscript i equals beta 0 plus beta 1 EO Subscript i plus u Subscript i​, where beta 0 is the intercept of the population regression​ line; beta 1 is the slope of the population regression​ line; u Subscript i is the error​ term; and the subscript i runs over​ observations, iequals​1, ...​ , n. For​ this, you collect data from a random sample of 300 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 4.94 and the variance of the number of times people eat out in a month is 4.04. You also find that the mean weight of people in the sample is 63.82 kg and the mean number of times people eat out in a month is 2.46. The OLS estimator of the slope beta 1 is nothing. ​(Round your answer to two decimal places​.)

Answer 1

The OLS estimator of the slope (beta 1), which represents the estimated relationship between people's weight and the number of times they eat out in a month, is 1.22 when rounded to two decimal places.

Step-by-step explanation:

To estimate the slope (beta 1) of the population regression line using the Ordinary Least Squares (OLS) method, we use the covariance of weight (W) and the number of times eating out (EO) divided by the variance of eating out (EO). Given the covariance is 4.94 and the variance is 4.04, the calculation for the slope would be:

slope (beta 1) = covariance / variance = 4.94 / 4.04

Therefore, the OLS estimator of the slope beta 1 is:

beta 1 = 1.22 (rounded to two decimal places)

Answer 2

The OLS estimator of the slope β₁ is 1.22.

Step-by-step explanation:

The OLS regression equation to estimate the relationship between​ people's weight ​(W​) and the number of times they eat out in a month ​(EO​) is:

`W=\beta_(0)+\beta_(1) EO_(i)+u_(i)`

The information provided is:

`Cov (W, EO)=4.94\\V(EO)=4.04\\E(W)=43.82\\E(EO)=2.46`

The formula to compute the OLS estimator of slope coefficient β₁ is:

`\hat \beta_(1)=(Cov(W, EO))/(V(EO))`

Compute the OLS estimator of slope coefficient β₁ as follows:

`\hat \beta_(1)=(Cov(W, EO))/(V(EO))=(4.94)/(4.04)=1.22277\approx1.22`

Thus, the OLS estimator of the slope β₁ is 1.22.