University of CaliforniaIrvine

Department of Economics

ECON 122A Econometrics I

Prof. Safarzadeh

HW #2Student Name:______

Solve the following problems:

1- Ten observations on the students’ number of hours of study a day and their average grade for the quarter has resulted in the following data:

Hours of Study: / 3 / 8 / 5 / 2 / 3 / 5 / 7 / 9 / 1 / 7
Grade: / 2 / 4 / 3 / 3 / 2 / 4 / 3 / 3 / 2 / 4

1-Do a scatter diagram of the relationship between the two variables.

2-Find the covariance between the two variables. What does it imply?

3-Find the correlation coefficient between the two variables. What does it imply?

4-Run a regression between the two variables and do a comprehensive analysis of the relationship between the two variables.

5-What is the effect of an hour of increase in study time on the students’ grade?

6-Do a forecasting of average grade for a student who studies only 4 hours a day.

2- In a study of 20 observations for the production technology of XYZ corporation the summary statistics for the relation between production (Q) and labor input (L) are given as:

Σ L = 320Σ Q = 1360Σ L2 = 103680 Σ Q2 = 1836000 Σ LQ = 436000

1-Do an OLS estimate of the production function.

2-Find the relevant statistics of the regression and the regression coefficients.

3-Find the relevant statistics of the regression and the regression coefficients.

4-XYZ is part of an industry that the marginal product of labor in the industry is 4 units. Do a hypothesis test (at the .05 level) that XYZ’s marginal product of labor is no different from the industry’s.

5-Write a 95% confidence interval for the estimated coefficient of L.

6-Do a forecasting of output if the labor input is 50 units.

3- In a study of the consumer behavior of 20 consumers the summary statistics for the relation between consumption (C) and income (Y) are given as:

ΣC = 1715000ΣY = 2392000Σ c2 = 1.35E+10Σ y2 = 3.53E+10

Σ yc = 1.67E+10

Where C and Y are consumption and income, respectively and c and y are the deviations of consumption and income form their corresponding means, respectively.

7-Do an OLS estimate of the consumption function.

8-Find the relevant statistics of the regression and the regression coefficients.

9-Find the relevant statistics of the regression and the regression coefficients.

10-Write a 95% confidence interval for the estimated coefficient of Y, the MPC.

11-Do a hypothesis test (at the .05 level) that the estimated MPC is less than 1.

12-Do a forecasting of consumption for a consumer whose annual income is $65000.

4- Prove that the estimated coefficient of X in the regression of Y = ßo + ß1X + u is BLUE (Best Linear Unbiased).

5- Prove that the estimated coefficient of X in the regression Y = ßo + ß1X + u will be the same as the estimated coefficient of Y in the regression X = αo + α1Y + e if and only if the R2 = 1.

6- Prove that the estimated residuals from the linear regression and the corresponding sample values of X are uncorrelated. That is, ΣXiei = 0, where ei is the estimated values of Ui.

6- Prove that in a two-variable regression model Y = ßo + ß1X + u, the R2 is the same as the square of the correlation coefficient between X and Y.

7- What is the effect on the estimated coefficient ß1 on the regression of Y on X, Y = ßo + ß1X + u:

a-if X is scaled by a factor of k.

b-if Y is scaled by a factor of k.

c-if both X and Y are scaled by a factor of k.

d-What will be the effect on the standard error of the coefficients, the t, F, and R2 statistics if the variables are scaled by a factor of k?

8- The following table represents the E-Views printout of the regression of US investment (INV)on GDP changes (DGDP) for the period 1984:1 to 2009:4.

Dependent Variable INV

Method: Least Squares

Sample (adjusted): 1984:1 2009:4

Included Observations: 99 after adjusting points

______

CoefficientStd. Error t-testProb.

______

C 13.01 1.821 7.31 0.013

DGDP 0.013 0.006 2.012 0.050

______

R-squared 0.69Mean Dependent Var. 355.90

Adj. R-squared 0.66 F Statistics 127.00

S.E. of Regression38.25Durbin Watson 1.53

______

a- Write the regression results in standard form.

b- Do a comprehensive statistical analysis of the model.

c- Do a comprehensive economic analysis of the model and its results.

d. What are the short-run and the long-run interest elasticity of investment in this model?

e. Write a 95% confidence interval for 2010:1 investment assuming that the GDP growth will be 4%.