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 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.
- 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?
- 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?
- 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?
- 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 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.
- 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.
- 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+ 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
————-+—————————— 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+ 15.19bdrms
- 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+ 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
————-+—————————— 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 profmarghave 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 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
- 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