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, iequals1, ... , 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.)

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warylucknow warylucknow · Answer 1 · 2020-03-16T08:58:30+01:00

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:

[tex]W=\beta_{0}+\beta_{1} EO_{i}+u_{i}[/tex]

The information provided is:

[tex]Cov (W, EO)=4.94\\V(EO)=4.04\\E(W)=43.82\\E(EO)=2.46[/tex]

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

[tex]\hat \beta_{1}=\frac{Cov(W, EO)}{V(EO)}[/tex]

Compute the OLS estimator of slope coefficient β₁ as follows:

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

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