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

Answer:

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:

$\hat \beta_{1}=\frac{Cov(W, EO)}{V(EO)}$

Compute the OLS estimator of slope coefficient β₁ as follows:

$\hat \beta_{1}=\frac{Cov(W, EO)}{V(EO)}=\frac{4.94}{4.04}=1.22277\approx1.22$

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