Question

can you please solve this

5.3 &7 (CH4, 44,41,425 Yweight it personi lets O hones。 1 ach person andoly soe ot th exercise times eresien modelY Lol turn Ui (b) 1, the fin+ te^ nts?"aru ans.rti.. E(..(x.)o Satistied

Answer 1

a) The term u_i represents the error associated with the i^th observation while predicting the weight of the i^th person using X_i as the independent variable.

b) The first least squares assumption is that the mean of residuals must be zero.

=> E(u_i|X_i) = 0

To calculate and check whether the mean of residuals is equal to zero, we can take the difference between expected and observed values of weights and take sum over it. If it is equal to zero we conclude that the mean of residuals is zero and E(u_i|X_i) = 0.

To know whether it is satisfied we would require the data.

c)   $\hat{Y}_i = 65 -3X_i$

This can be interpreted that when X_i = 0 i.e the person performs 0 hours of exercise the expected weight of the person is 65.

and when X_i = 1 i.e the person performs 1 hour of exercise then the expected weight of the person is 62.