# 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.*

- 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
*meduc*and*feduc*xed, 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
*meduc*and*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.

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

*price*= _{0}+ _{1}*sqrft *+ _{2}*bdrms *+ *u*

where*price *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?

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

*rdntens*= _{0}+ _{1}*lsales *+ _{2}*profmarg *+ *u*

where*rdintens*is R&D spending as a percent of total sales, *lsales*is the log of sales, and *profmarg*are 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
*profmarg*have a statistically signicante⁄ect on*rdintens*?

- An intern working for you turns in the following:

- What is the
*R*^{2}? - What is the standard error of the regression, ^?
- What is the standard error of b1?

- 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.*

- 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

————-+—————————— Adj R-squared = 0.2108

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

——————————————————————————

- Write down the estimated regression equation.

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

- 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.

- Holding
*meduc*and*feduc*xed, 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.

- Explain the interpretation of the coe¢ cient on
*meduc*and*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.

- 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 .

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

*price*= _{0}+ _{1}*sqrft *+ _{2}*bdrms *+ *u*

where*price *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

————-+—————————— Adj R-squared = 0.6233

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

——————————————————————————

- Write down the estimated regression equation.

*price*= _{-19.3}+ _{0.12*}*sqrft*+ _{15.19}*bdrms*

- 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.

- 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.

- 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.

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

Now the price would be 335.26

- 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.

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

*rdntens*= _{0}+ _{1}*lsales *+ _{2}*profmarg *+ *u*

where*rdintens*is R&D spending as a percent of total sales, *lsales*is the log of sales, and *profmarg*are 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

————-+—————————— Adj R-squared = 0.0363

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

——————————————————————————

- 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.

- 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

————-+—————————— Adj R-squared = 0.0124

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.

- 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 .

- Does
*profmarg*have a statistically signicante⁄ect on*rdintens*?

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

- An intern working for you turns in the following:

- What is the
*R*^{2}?

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

- 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