Suppose we have a random sample of 50 people and their

Reference no: EM13378798

Suppose we have a random sample of 50 people and their weight, W and height, H are recorded to the nearest pound and inch respectively. A regression of W on H and an intercept gives:

Wi = 99.41(6.45) + 3.94(1.86)Hi

R^2 = 0.81, SER = \(\sqrt{Su^2}\) = 10.1

(Standard errors are given in parentheses)

(a). What is the prediction of the weight of someone who is 50inches tall, 60inches tall, 70 inches tall?

(b). What is the prediction for the change in weight of someone who grows 1.5 inches? What is the predicted difference in weight between 2 people who differ by 6 inches in height?

(c). Suppose that the sample average of H is 56 inches. What is the sample average of W? Why?

(d). Perform 2-sided t-tests for the null hypothesis that the slope is zero at the 5% and 1% significance levels and interpret the results.

(e). Perform 1-sided t-tests for the null hypothesis that the slope is zero at the 5% and 1% significance levels and interpret the results. Ensure you justify the use of a 1-sided test.

(f). Explain the potential advantage in relation to the sizes of Type I and Type II errors of using a 1-sided t test rather than a 2-sided t-test if a one-sided test is justified. [Diagrams are likely to be helpful.]

(g). Suppose we measured weight in kilos. What will the new intercept be?

(h). Prove that if Wi = \(\lambda1 + \lambda2Wi\lambda\) \(\lambda1 + \lambda2b1\) where b1 is the intercept of the original regression of W on H.

(i). Explain how the standard error of the slope coefficient in () is related to the standard error of the slope in the original regression.

(j.) Suppose that in addition to measuring weight in kilos we also measured height in centimetres. What would the new slope estimate be?

(k). Prove that if W1 = \(\lambda1 + \lambda2Wi\) and Hi = \(\mu1 + \mu2Hi\) then the new slope is b2 = \((\lambda2/\mu2)b2\)

where b2 is the slope of the original regression of W on H.

(l). What will R^2 be in the regression you considered in (j)? Why?

(m). Explain how the OLS estimator of the variance of the disturbance term in (k) is related to that in (h).

(n). Explain how the standard error of the slope coefficient in (k) is related to that in (h).

Reference no: EM13378798

Questions Cloud

An electronic device is available that will reduce this : an electronic device is available that will reduce this years labor cost by 10000. the equipment is expected to last

Swapna david is a customer assistant consultant for acme : swapna david is a customer assistant consultant for acme information systems who provides assistance for computer

Greener grass company ggc competes with its main rival : greener grass company ggc competes with its main rival better lawns and gardens blg in the supply and installation of

A contractor submits a bid on a project for which more : a contractor submits a bid on a project for which more research and development work needs to be done. it is estimated

Suppose we have a random sample of 50 people and their : suppose we have a random sample of 50 people and their weight w and height h are recorded to the nearest pound and inch

In avataria the main source of income is hunting avatarians : in avataria the main source of income is hunting. avatarians have an option to improve their hunting skills by training

Based on grossly distorted picture how useful do you think : based on grossly distorted picture how useful do you think gdp is as an economic indicator? what are its limitations as

The machining time per piece if 0164 h and the machine : the machining time per piece if 0.164 h and the machine loading time is 0.038h. with an operator rate of 12.80h and a

At a particular academically challenging high school the : at a particular academically challenging high school the average gpa of a high school senior is known to be normally

User Account

All Pages