Managerial Economics-Regression Analysis

QUESTION 1:

Copy the database below into an excel sheet.

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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 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