Econ/Stat questions HELP

Part I: Answer problems 1-3 (30 points each):

1. “In July 2021, the United States Department of Labor reported that the Consumer Price Index (CPI) rose 5.4%. The increase in consumer prices was the largest jump since August of 2008…”. Use the appropriate Bureau of Labor Statistics (BLS) table posted in the ‘Class Exhibits, Diagrams, Charts… ‘module on the class canvas site to respond to parts 1a and 1b:

1a. i) At what rate did the CPI rise from August 2008 to July 2021? ii) What does this rise represent? iii) Identify the bit of useful information missing from the first sentence of the quotation.

1b. What was the average annual rate increase in the CPI over that time? (Note: for simplicity of calculation assume that the time period was exactly 13 years).

2. A random sample of incomes, n = 11, expressed in $ ,000’s, and drawn from a large population, (N > 12,000) includes the following data points:

32, 19, 40, 22, 24, 16, 11, 8, 0, 14, 78

A) What is the variance of the observations in this sample? Show all of your calculations. What does the variance represent for this sample?

B) What is the standard deviation for this sample? What does the standard deviation represent for this sample?

3. The following table presents the results of a regression using gretl data3-7.gdt:

Regression of cost of repairs (cost, in dollars) on miles driven (in ’000’s of miles):

Model 1: OLS, using observations 1-57 Dependent variable: cost

	Coefficient	Std. Error	t-ratio	p-value
Const	−796.075	134.745	−5.908	<0.0001	***
Miles	53.4507	2.92614	18.27	<0.0001	***

Mean dependent var	1426.632		S.D. dependent var	1151.186
Sum squared resid	10501755		S.E. of regression	436.9680
R-squared	0.858491

a. Interpret the results of this regression, as we have in class, for: coefficient, standard error, and t-ratio of the independent variable; r2, and S.E. of regression.

b. Express the regression as an equation.

c. Is the estimate of the independent variable statistically significant? How can you tell? Interpret the value of the independent variable, and its statistical significance.

Part 2: Answer either problem 4 or problem 5 (10 points).

4. Consider a normally distributed sample data set, with n = 244, mean of 147, and standard deviation of 12. Calculate the range of values around the mean that would capture about 95% of the data in the sample. Interpret your result.

5. Two graphs in a recent issue of the Economist magazine indicate that, as Vietnam’s merchandise exports increased from near zero in 1995 to about $200 billion (in US dollars) in 2020, per capita GDP in Vietnam by a factor of 5. The magazine went on to conclude that trade and foreign investment helped Vietnam emerge from poverty. Based on the graphs, did the magazine draw a valid conclusion?