Reference no: EM132750964

TECO201 Elements Of Econometrics - Australian National Institute of Management and Commerce

Question 1
Part a)
Find the following probabilities by checking the z table i) P (0.65<Z<1.45)
ii) Z0.15

Part b)
The amount of time the university professors devote to their jobs per week is normally distributed with a mean of 52 hours and a standard deviation of 6 hours.
i) What is the probability that a professor works for more than 60 hours per week?
ii) Find the probability that the mean amount of work per week for three randomly selected professors is more than 60 hours?

Part c)

A statistics practitioner is in the process of testing to determine whether is enough evidence to infer that the population mean is different from 180. She calculated the mean and standard deviation of a sample of 200 observations as X =175 and s=22.

Calculate the value of the test statistic of the test required to determine whether there is enough evidence to infer at the 5% significance level that the population means is different from 180.

Question 2

You are given the following data based on 10 pairs of observations on Y and X.

∑ Y_?? = 507, ∑ X_?? = 5600, ∑ X_??Y_??  = 305550

∑ X² = 4760000 , ∑ Y² = 26071

Assuming all the assumptions of CLRM are fulfilled, obtain
i) b1 and b2
ii) Standard error of the regression (SER)
iii) Standard errors of these estimators (b1 and b2).

Question 3

Based on the data for years 1962 to 1977 for the United States, economists obtained the following demand function for automobiles:

Yi(hat) = 5807 + 3.24Xi r2 = 0.22 se = (1.634)

where Y = retail sales of passenger cars (thousands) and X = the real disposable income (millions dollars).
Note: The se for b1 is not given.

i) Interpret the estimated intercept and slop
ii) How would you interpret r2?
iii) Establish a 95% confidence interval for B2.
iv) Compute the t value under H0:B2 = 0. Is it statistically significant at the 5 precent level? Which t test do you use, one tailed or two-tailed, and why?

Question 4
A three-variable regression gave the following results:

Source of variation	Sum of squares (SS)	d.f.	Mean sum of squares (MSS)
Due to regression (ESS)	65,965	---	---
Due to residual (RSS)	---	---	---
Total (TSS)	66,042	14

Source of variation Sum of squares (SS) d.f. Mean sum of squares (MSS)
Due to regression (ESS) 65,965 --- ---
Due to residual (RSS) --- --- ---
Total (TSS) 66,042 14

a. What is the sample size?
b. What is the value of the RSS?
c. What are the d.f. of the ESS and RSS?
d. What is R2? And adjusted R2?

Attachment:- Elements Of Econometrics.rar