Question

In: Economics

A researcher estimated the following regression model with a sample size of 36. ?? = ?0...

A researcher estimated the following regression model with a sample size of 36. ?? = ?0 + ?1??1 + ?2??2 + ? The researcher wanted to find out whether there is heteroscedasticity in the error variance and so applied the White’s heteroscedasticity test. The result is as follows: ?? = −5.8417 + 2.5629??1 + 0.6918??2 − 0.4081??1 2 − 0.0491??2 2 + 0.0015??1??2 R 2 = 0.2143 What conclusion can you assist the researcher to draw at 5 percent and 10 percent?

Solutions

Expert Solution

Answer,

For given regression equation of ui, we need to check whether the obtained equation is overall significant.

We can set the null hypothesis as

H0: b1=b2=b3=b4=b5=0

H1: at least one bi =! 0 (for i =1, 2, 3, 4, 5)

Symbol "=!" means "not equal to".

Now we will calculate F-statistic.

Formula for F-statistic = R-sqaured/(1-R-squared)*(n-p)/p

n= sample size, p =number of parameters

n=36 and p=5

F-statistic = 0.2143/(1-0.2143)*(36-5)/(5-1) = 0.2143*31/(0.7857*4)= 2.1138

Now, we will check for critical value of F-statistic for 5% and 10% significance level

Critical F-statistic for 10% level (4,31) = 2.136

Critical F-statistic for 5% significance level(4,31) = 2.679

For 5% significance, Critical F=2.68 is greater than Calculated F =2.11, therefore we cannot reject the null hypothesis

For 10% significance, Critical F=2.136 is greater than Calculated F =2.11, therefore we cannot reject the null hypothesis

hence, we can admit that there is no heteroskedasticity in this model.


Related Solutions

ECONOMETRICS 2 1) Consider the following estimated regression equation where the sample size is 78 (quarterly...
ECONOMETRICS 2 1) Consider the following estimated regression equation where the sample size is 78 (quarterly data): IND - OUTPUT (dependent variable): Industrial Production Index. PRICE (independent variable): Industrial Price Index. LOGIND-OUTPUT= -76.5- 0.39 LOG(PRICE)                 t statistics:                                 (-1.35)    (-0.72)          a) Interpret and test the coefficient of LOG(PRICE)?        Assume that an additional regression was run as: LOGIND-OUTPUT= -33.5 +0.46 LOGPRICE+0.009 T                 t statistics:                          (-4.63)    (2.78)                        (3.55) where T is a time trend. b) Interpret the coefficient of T...
for a fixed sample size as the number of indeoendent variables in a regression model increases...
for a fixed sample size as the number of indeoendent variables in a regression model increases the power of the regression decreases. T or F The width of a 95% confidence interval around a relative risk increases as the sample size decreases. T or F
1. Consider the linear regression model for a random sample of size n: yi = β0...
1. Consider the linear regression model for a random sample of size n: yi = β0 + vi ; i = 1, . . . , n, where v is a random error term. Notice that this model is equivalent to the one seen in the classroom, but without the slope β1. (a) State the minimization problem that leads to the estimation of β0. (b) Construct the first-order condition to compute a minimum from the above objective function and use...
In a study for housing demand, the following regression model was estimated. The standard errors of...
In a study for housing demand, the following regression model was estimated. The standard errors of each coefficient are shown in the parentheses below. log Qt = 4.17 – 0.24 log Pt + 0.96 log Yt + 0.46 log MOR15t - 0.52 MOR30t + εt (0.03) (0.32) (0.23) (0.40) Adj R 2= 0.84, DW = 2.75, N=30. Where, Q = quantity of housing demanded P = price of unit of housing Y = family income MOR15 = 15-year mortgage rate...
Consider the simple regression model ? = ?0 + ?1? + ?) In the following cases,...
Consider the simple regression model ? = ?0 + ?1? + ?) In the following cases, verify if the ‘zero conditional mean’ and ‘homoscedasticity in errors’ assumptions are satisfied: a. If ? = 9? where ?(?⁄?) = 0, ???(?⁄?) = ? 2 b. If ? = 5.6 + ? where ?(?⁄?) = 0, ???(?⁄?) = 3? 2 c. If ? = 3?? where ?(?⁄?) = 0, ???(?⁄?) = ? 2 2) D. In which of the cases above are we...
Explain the differences between the regression model, the regression equation, and the estimated-regression equation. Discuss the...
Explain the differences between the regression model, the regression equation, and the estimated-regression equation. Discuss the application of regression analysis in business decision making. Give examples on how the regression analysis can be used in business.
You are given the following output for a multiple regression based on a sample of size...
You are given the following output for a multiple regression based on a sample of size n = 10 Predictions Coefficients Standard Error Constant -0.58762 x1 b1=1.510 0.351 x2 b2=-0.245 0.157 x3 b3=1.823 0.836 SSR=17.56; SSE=8.56 (a) Calculate a 90% confidence interval for β1. Provide a clear interpretation of the interval. (b) Which predictor variable(s) – x1, x2, x3 – should be kept in the regression model and why, if testing at a 5% level of significance? (use two-sided tests)...
2008 2007 Sample Size 36 36 Sample Mean 75.0000 70.7500 Sample Standard Deviation 17.2891 8.7843 df...
2008 2007 Sample Size 36 36 Sample Mean 75.0000 70.7500 Sample Standard Deviation 17.2891 8.7843 df 51 Confidence Interval (in terms of 2008 - 2007) Confidence Coefficient 0.80 Lower Limit 0.0535 Upper Limit 8.4465 Hypothesis Test (in terms of 2008 - 2007) Hypothesized Value 0 Test Statistic p-value (Lower Tail) p-value (Upper Tail) p-value (Two Tail) 2008-2007 Sample Size 36 Sample Mean 4.2500 Sample Standard Deviation 20.2969 Confidence Interval (in terms of 2008 - 2007) Confidence Coefficient 0.80 Lower Limit...
Distinguish between the following: Heteroskedasticity and autocorrelation specified regression model vs estimated regression equation data type...
Distinguish between the following: Heteroskedasticity and autocorrelation specified regression model vs estimated regression equation data type vs level of measurement ANOVA and Multiple Regression Outliers vs Influencers
Distinguish between the following: Heteroskedasticity and autocorrelation specified regression model vs estimated regression equation data type...
Distinguish between the following: Heteroskedasticity and autocorrelation specified regression model vs estimated regression equation data type vs level of measurement ANOVA and Multiple Regression Outliers vs Influencers Based on question 1e above, do you think the following scatter plots contain any outliers or any influential data points? Justify your answers on each plot. (iii)                                                                                          (iv) (i)                                                                                            (ii)      
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT