# Estimated Regression Equation

Be very precise in your answers and show all of your work where necessary. For the computer based problems using Stata, print o⁄ and turn in your results output and code along with your answers to the specific questions.

1. Using the posted data set WAGE2.DTA, estimate a model where you regress years of education (educ) on the number of siblings (sibs), mother s education (meduc), and father s education (feduc).
• Write down the estimated regression equation.
• Is the sign on the parameter estimate for sibs what you would expect? Explain.
• Holding meducand feducxed, by how much does sibs have to increase to reduce predicted years of education by one year (it is ok if you get a noninteger answer)?
• Explain the interpretation of the coe¢ cient on meducand feduc.
• Suppose that individual A has no siblings and his mother and father each have 12 years ofeducation. Now suppose that individual B has no siblings and his mother and father each of 16 years of education. What is the predicted di⁄erence in years of education between individuals A and B? Show your work.
2. Use the posted data set HPRICE1.DTA to estimate the model

price= 0+ 1sqrft + 2bdrms + u

whereprice is the house price measured in thousands of dollars.

• Write down the estimated regression equation.
• What is the estimated increase in price for a house with one or more bedrooms, holding squarefootage constant?
• What is the estimated increase in price for a house with an additional bedroom that is 140 squarefeet in size? Compare this to your answer in part (b).
• What percentage in the variation in price is explained by square footage and the number ofbedrooms?
• Suppose a house has sqrft= 2;438and bdrms= 4: Find the predicted selling price for this house.
• The actual selling price for the house in part (e) was \$300;000(so price = 300). Find the residual for this house. Does this suggest that the purchaser underpaid or overpaid for this particular house?
1. Use the posted data set RDCHEM.DTA to estimate the model

rdntens= 0+ 1lsales + 2profmarg + u

whererdintensis R&D spending as a percent of total sales, lsalesis the log of sales, and profmargare pro ts as a percent of sales.

• Interpret the coe¢ cient on lsales. In particular, if sales increases by 10%, what is the estimated percentage point change in rdintens? Is this economically a large e⁄ect?
• Test the hypothesis that R&D intensity (rdintens) does not change with sales against the alternative that it does increase with sales. Do the tests at the 5% and 10%
• Interpret the coe¢ cient on profmarg. Is it economically signicant?
• Does profmarghave a statistically signicante⁄ect on rdintens?
1. An intern working for you turns in the following: • What is the R2?
• What is the standard error of the regression, ^?
• What is the standard error of b1?
1. Consider the following: • Compute b0 and b1: 1
• Test the hypothesis that = 1. Use the 5% level of signicance.

Solution

Be very precise in your answers and show all of your work where necessary. For the computer based problems using Stata, print o⁄ and turn in your results output and code along with your answers to the speci c questions.

1. Using the posted data set WAGE2.DTA, estimate a model where you regress years of education (educ) on the number of siblings (sibs), mother s education (meduc), and father s education (feduc).

regeducmeducfeduc sibs

Source |       SS       df       MS              Number of obs =     722

————-+——————————           F(  3,   718) =   65.20

Model |  772.281437     3  257.427146           Prob> F      =  0.0000

Residual |  2834.93324   718  3.94837499           R-squared     =  0.2141

Total |  3607.21468   721  5.00307168           Root MSE      =  1.9871

——————————————————————————

educ |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]

————-+—————————————————————-

meduc |   .1307872    .032689     4.00   0.000     .0666098    .1949646

feduc |   .2100041   .0274748     7.64   0.000     .1560635    .2639447

sibs |  -.0936359   .0344713    -2.72   0.007    -.1613124   -.0259594

_cons |   10.36426   .3585001    28.91   0.000     9.660422    11.06809

——————————————————————————

1. Write down the estimated regression equation.

Educ= 10.3 +0.130*meduc+0.21*feduc-0.093*sibs

1. Is the sign on the parameter estimate for sibs what you would expect? Explain.

Yes we expect that because if we have siblings , then its not easy to study because we are always caught up in fun things.

1. Holding meducand feducxed, by how much does sibs have to increase to reduce predicted years of education by one year (it is ok if you get a noninteger answer)?

We have to increase the siblings by 10 times , because the proportional effect is 0.1 so , ten times would make that 1.

1. Explain the interpretation of the coe¢ cient on meducand feduc.

When there are mother or father who are educated in home , they always push their son/ daughter to study hard and moreover they can easily guide you so in that case the education of self will increase.

1. Suppose that individual A has no siblings and his mother and father each have 12 years ofeducation. Now suppose that individual B has no siblings and his mother and father each of 16 years of education. What is the predicted di⁄erence in years of education between individuals A and B? Show your work.

According to equation A will have education of 10.3+ 0.13*12+0.21*12 = 15.58

B will have education of , 10.3 + 16*0.44 = 17.34 , difference will be , 1.76 .

1. Use the posted data set HPRICE1.DTA to estimate the model

price= 0+ 1sqrft + 2bdrms + u

whereprice is the house price measured in thousands of dollars.

reg price sqrftbdrms

Source |       SS       df       MS              Number of obs =      88

————-+——————————           F(  2,    85) =   72.96

Model |  580009.152     2  290004.576           Prob> F      =  0.0000

Residual |  337845.354    85  3974.65122           R-squared     =  0.6319

Total |  917854.506    87  10550.0518           Root MSE      =  63.045

——————————————————————————

price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]

————-+—————————————————————-

sqrft |   .1284362   .0138245     9.29   0.000     .1009495    .1559229

bdrms |   15.19819   9.483517     1.60   0.113    -3.657582    34.05396

_cons |    -19.315   31.04662    -0.62   0.536    -81.04399      42.414

——————————————————————————

1. Write down the estimated regression equation.

price= -19.3+ 0.12*sqrft+ 15.19bdrms

1. What is the estimated increase in price for a house with one or more bedrooms, holding squarefootage constant?

With increase breadroomsize , the price increase by 15 units.

1. What is the estimated increase in price for a house with an additional bedroom that is 140 squarefeet in size? Compare this to your answer in part (b).

The price would increase by 0.12 * 140 = 16.8 units.

1. What percentage in the variation in price is explained by square footage and the number ofbedrooms?

63 % of the variation is explained by independent variables.

1. Suppose a house has sqrft= 2;438and bdrms= 4: Find the predicted selling price for this house.

Now the price would be 335.26

1. The actual selling price for the house in part (e) was \$300;000(so price = 300). Find the residual for this house. Does this suggest that the purchaser underpaid or overpaid for this particular house?

Residual would be 35.26 , so purchaser overpay.

1. Use the posted data set RDCHEM.DTA to estimate the model

rdntens= 0+ 1lsales + 2profmarg + u

whererdintensis R&D spending as a percent of total sales, lsalesis the log of sales, and profmargare pro ts as a percent of sales.

. regrdintenslsalesprofmarg

Source |       SS       df       MS              Number of obs =      32

————-+——————————           F(  2,    29) =    1.58

Model |   10.717099     2  5.35854952Prob> F      =  0.2224

Residual |  98.1163713    29  3.38332315           R-squared     =  0.0985

Total |   108.83347    31  3.51075711           Root MSE      =  1.8394

——————————————————————————

rdintens |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]

————-+—————————————————————-

lsales |   .3213484   .2155689     1.49   0.147    -.1195395    .7622362

profmarg |   .0500367   .0457768     1.09   0.283    -.0435874    .1436608

_cons |   .4722541   1.676056     0.28   0.780    -2.955665    3.900174

——————————————————————————

1. Interpret the coe¢ cient on lsales. In particular, if sales increases by 10%, what is the estimated percentage point change in rdintens? Is this economically a large e⁄ect?

If sales increase by 10% , there will be 3.21 % change . it is quite large as costs are quite high.

1. Test the hypothesis that R&D intensity (rdintens) does not change with sales against the alternative that it does increase with sales. Do the tests at the 5% and 10%

. regrdintens sales profmarg

Source |       SS       df       MS              Number of obs =      32

————-+——————————           F(  2,    29) =    1.19

Model |  8.28423732     2  4.14211866           Prob> F      =  0.3173

Residual |  100.549233    29  3.46721493           R-squared     =  0.0761

Total |   108.83347    31  3.51075711           Root MSE      =   1.862

——————————————————————————

rdintens |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]

————-+—————————————————————-

sales |   .0000534   .0000441     1.21   0.236    -.0000368    .0001435

profmarg |   .0446166   .0461805     0.97   0.342    -.0498332    .1390664

_cons |   2.625261   .5855328     4.48   0.000     1.427712     3.82281

So now regression says that , the coeff of sales is not significant means that , the price wont change with sales. Thus we accept null hypo.

1. Interpret the coe¢ cient on profmarg. Is it economically signicant?

Yes it is significant because the profit margin is 5 % that’s feasible and achievable .

1. Does profmarghave a statistically signicante⁄ect on rdintens?

No it does not  have sig effect because it is not statistically significant.

1. An intern working for you turns in the following: • What is the R2?

8/10= 80 %

• What is the standard error of the regression, ^?

Standard error would be Se / root of (32) = 0.2/root (1/102)  = 2.01

• What is the standard error of b1?

Standard error would be Se / root of (32) = 2 /10*(4 ) = 0.05

1. Consider the following: • Compute b0 and b1: 1

B1 = sxy *sxy / sxx * syy = 30*30/(100*60) = 0.15 , bo = 20 – 10*0.15= 18.5

• Test the hypothesis that = 1. Use the 5% level of signicance

Not mentioned what we need to test. Sorry