Reference no: EM13179589
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).
|
What is the uniform annual equivalent value
: An electronic device is available that will reduce this year's labor cost by $10,000. The equipment is expected to last for 8 years. If labor costs increase at an average rate of 7% per year and the interest rate is 12% per year: a. What is the m..
|
|
Find probability that she will have to obtain her cup of tea
: Swapna David is a customer assistant consultant for Acme Information Systems, who provides assistance for computer users. The mean number of calls per hour is 40 from across the United States and calls are independent.
|
|
Derive the demand curves for ggc''s product in each market
: Plot graphically the demand and MR curves for each market, and also show GGC's combined marginal revenue curve (?MR) and its MC curve. Show graphically the quantities that should be produced and sold, and the prices that should be charged, in each..
|
|
What will be the standard deviation of the profit made
: A contractor submits a bid on a project, for which more research and development work needs to be done. It is estimated that the total cost of satisfying the project specifications will be $20 million, plus the cost of the further research and dev..
|
|
What is the prediction of the weight of someone
: 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 sampl..
|
|
What is the total number of turkeys caught by avatarians
: Assume an avatarian with no training can catch 1 turkey per month. How many turkeys per month can an avatarian with 5 years of training catch? With 8 years of training? With 10 years of training? With 15 years of training? (b) Assume there are 100..
|
|
How is the human development index
: What are its limitations as an economic measurement? How is the Human Development Index (HDI) a better barometer of economic well-being? What are its advantages and disadvantages?
|
|
Calculate the optimal number of machines for the lowest cost
: The machining time per piece if 0.164 h, and the machine loading time is 0.038h. With an operator rate of $12.80/h and a machine rate of $14/h, calculate the optimal number of machines for the lowest cost per unit of output.
|
|
Develop a 90% confidence interval for population mean gpa
: At a particular academically challenging high school, the average GPA of a high school senior is known to be normally distributed with a variance of 0.25. A sample of 20 seniors is taken and their average GPA is found to be 2.71
|