Exercises5.1 Suppose that a rescarcher, using data on class size (CS) and average testscores from 100 third-grade classes, estimates the OLS regressionTestScore- 520.4 - 5.82 x CS, R² =0.08, SER = 11.5.(20.4) (2.21)a. Construct a 95% confidence interval for B, the regression slope coef-ficient.b. Calculate the p-value for the two-sided test of the null hypothesisHs B1 -0. Do you reject the null hypothesis at the 5% level? At the1% level?

(A). The regression slope coefficient is given by β and the class interval at 95% is to be…

Answered: 51 Suppose that a rescarcher, using…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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(e) Suppose you have been given the following ordinary least squares (OLS) regression result. Estimated Long Run Coefficients using the ARDL Approach ARDL (1,2,2,2,0,2) selected based on Akaike Information Criterion Dependent variable is LY 33 observations used for estimation from 1987 to 2019 T-Ratio [Prob.] 4.6671[0.000] 4.6678[0.051] 7.9897[0.043] -4.802[0.009] 2.3898[0.028] 1.0498[0.308] Regressor Coefficient Standard Error 0.36068 0.45447 LK 0.077280 LM 0.097363 0.48751 -0.41208 0.19057 0.52521 LE 0.061017 LF 0.085800 LT 0.079744 C 0.500320 where, Y = Economic growth K = Capital M = Employment E = Electricity consumption F = Foreign direct investment T= Technology (i) Write the regression equation. Interpret the estimated coefficients. (ii) Which explanatory variables are significant at the 1%, 5% and 10% level? Which variables are insignificant? Briefly explain.
Test whether the slope coefficient in both Model is statistically significant at 10% significance level.
Consider the following computer output of a multiple regression analysis relating annual salary to years of education and years of work experience. Regression Statistics Multiple R 0.7339 R Square 0.5386 Adjusted R Square 0.5185 Standard Error 2137.5200 Observations 49 ANOVA SS df Regression 2 245,370,679.3850 122,685,339.6925 26.8517 MS F Significance F 1.9E-08 Total Residual 46 210,173,612.6150 48 455,544,292.0000 4,568,991.5786 Coefficients Standard Error Intercept Education (Years) 14290.37278 2350.8671 2,528.5819 338.1140 Experience (Years) 829.3167 392.5627 t Stat P-value 5.6515 0.000000961 9200.6014 6.9529 0.000000011 2.1126 0.040093183 Lower 95 % Upper 95% 19,380.1442 1670.2789 3031.4553 39.129 1619.5044 Step 2 of 2: How much would you expect your salary to increase if you had one more year of education?
determine the regression line equation plot the line on a graph and summarize the results( reject or do not) is there enough evidence?
You use a dataset with 538 observations to run a simple linear regression. You find that the coefficient estimate is 3.258 and that the standard error of the coefficient estimate is 1.794. What is the lower end of the 98% confidence interval (of a two- sided test)? (you need to write a number that is rounded to the fourth digit after the decimal).
1. Suppose have the sample linear regression function: we Y = B, + B,X, +e,, Bo and B are OLS estimates, prove the following equations hold: Ee, = 0 а. %3D b. Se,x, = 0, x, is the deviation form of Xi EeÝ, = 0 c. d. Y = Y 2. Suppose the sample size n=10, we have the following figures for the sample data: ΣΥ-1110; ΣΧ-1 680; ΣΧY -204200 | ΣΧ31 5400; ΣΥ-133300 The representation of PRF is Y = b, +b,X, +u,, u, O iid N(0,4) The OLS estimates for the SRF is ß, and B a. calculate B, and B with the above figures. b. calculate the standard error of B, and B- c. calculate the determination coefficient: R? d. construct 95% confidence interval for b, and b, respectively. e. conduct hypothesis test: HO: b, =0, H1: b, #0. f. conduct hypothesis test: HO: b, =1, H1: b, #1.
The OLS estimation of the relationship between GRADE and HOURS of studying gives the following fitted equation (standard errors in parentheses): GRADEA = 38.15+0.048*HOURS (6.85) (0.01) Calculate the corresponding t statistic to test the slope coefficient for significance (Use two decimal places without rounding)
2
A researcher investigating whether government expenditure crowds out investment estimates a regression on data for 30 countries. I-investment; G-government recurrent expenditure; Y=gross domestic product; all measured in $US billion. P= population measured in million. Standard errors are in parentheses. Î= 18.10 (7.79) R² = 0.99 1.07G + 36Y (0.14) (0.02) She suspects that countries with higher GDP may have more variability in their investment. She sorts the observations by increasing size of gdp per capita (Y)and estimates the regression again for the 11 countries with the lowest gdp(Y)and the 11 countries with the largest gdp(Y). The RSS1 from the first regression is 7186. The RSS2 from the second regresison is 28101. Perform a Goldfeld-Quandt Test at a 5% significance level. a. The test statistic for this test is 0.256 b. The critical value defining the rejection region for Ho is 3.18 c. Is there heterscedasticity? Yes=1 or No-0. The answer is 0
V3
Construct a 95% confidence interval for the average value of y for the following data. Use x = 25, se = 4.40, and the equation of the regression line, = 16.394 +0.196x. x 14 21 28 9 20 y 17 16 22 19 26 (Do not round the intermediate values. Round your answers to 2 decimal places, e.g. 0.75.) SE(Y25) s
3

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