Managerial Economics-Regression Analysis

QUESTION 1:

Copy the database below into an excel sheet.

Run QX on the four regressors: PX, M, PY and lagged Qx.

Write down the estimated linear demand equation with t-statistics under the estimated coefficients as done above. In addition, write down the R-square and explain what it means. Explain the statistical significance of the t-statistics for each regressor. Significance of T-statistics is usually given by the P-values in the regression output. We will not use it in here because we have a small sample which will bias the P-values. There are three levels of significance: 1%, 5% and 10% represented by ***, ** and *, respectively. Do not use the computed P-values of this small sample regression. Instead, use the following conventional t-statistics significance ranges used for large data:1.63 <t < 1.96 (10%); 1.96 < t < 2.54 (5%); and t > 2.54 (1%). This means in your regression output, look at the t-statistics column for each regressor. Then place the value of that computed t-statistic in one of the above ranges. The P-values given in the regression output are sensitive to sample size and are not accurate.

 

QUESTION 2

Check the signs of the estimated coefficients. Do the signs follow the theory as expected? Examine the sign for each regressor and point out what they mean.

 

 

QUESTION 3:

Calculate the short-run and long-run price and income elasticities of demand for good X using the averages for the quantity, price and income? Based on the income elasticity, what type is good X?

 

Short Run P elasticity for a linear Eq. = [slope of price]*(Average Price/Average quantity)

 

Long Run P elasticity for a linear Eq. = (SR P elasticity) /(1- slope of lagged Q)

 

or = [slope of price / (1- slope of the lagged variable)]*(Average Price/Average quantity).

 

They are the same.

Average = sum/n, skipping first row.

 

The short-run and long run income elasticities are calculated the same way. Here the slope is for income and the average for income (see page 31 or the solved regression on pp 32-33). What type of good is X with respect to income elasticities?

 

Short Run Income elasticity for a linear Eq. = [slope of Income]*(Average Income/Average quantity)

 

Long Run Income elasticity for a linear Eq. = (SR Income elasticity)/(1- slope of lagged Q)

 

 

QUESTION 4:

Calculate the short-run and long-run cross price elasticities with respect to Py (see p. 28 and p. 30 in the notes). What type of goods are X and Y with respect to these elasticities?

 

QUESTION 5

Can you think of another independent variable that you may add to the above equation? What will the sign of this variable be? Specify the name of this variable. Do not include Weather in this equation.

 

QUESTION 6

Is this a supply or demand equation? Why? Forget about signs. Look for other clues in the equation.

 

 

SEE DATA BELOW:

 

Copy the data from Word to excel.

After transferring the data set from Word to excel, make sure you follow these steps;

Highlight all the cells in excel.

Right click on any cell in the data sheet in excel.

Click on FORMAT CELLS.

Under CATEGORY, click on NUMBER.

Then click OK.

 

Spring 2010: Regression Assignment Data Sheet (linear case only))

When you copy in Excel 2007: COPY, PASTE SPECIAL then TEXT.

 

 

 

Year	Qx	Px	M	Py	Lagged QX
1984	9	29	14	11
1985	10	28	15	12	9
1986	12	25	18	14	10
1987	14	23	20	15	12
1988	16	20	23	17	14
1989	17	19	26	19.5	16
1990	18	17	29	21	17
1991	21	16	34	22	18
1992	26	14	37	23	21
1993	28	12.5	35	23.5	26
1994	29	12	38	25	28
1995	30	10	41	23	29
1996	33	14	44	20	30
1997	35	15	47	19	33
1998	38	18	51	20	35
1999	39	19	55	21	38
2000	40	21	58	22	39
2001	42	18	61	23	40
2002	45	18	63	25	42
2003	46	17	65	26	45
2004	50	15	66	21	46
2005	55	14	68	25	50
2006	57	12	70	27	55
2007	58	10	73	28	57
2008	61	9	74	28.5	58
2009	65	8.5	79	30	61
2010	66	7	80	31	65