Question

Can you do problem 20 and 21, problem 18 and and 19 is there for reference, Thank you!

Question 18 3 pts Consider the following OLS multiple regression results from Table 2 of “The Impact of Light Skin on Prison Time for Black Female Offenders" (The Social Science Journal 48 (2011), p. 256]. The dependent variable is the natural logarithm of time served, where time served is measured as the number of days served in prison. At the time of admission to prison, correctional officers noted whether female African- American inmates had light skin tones or not, and denoted whether a prisoner was thin (in terms of body weight) or not. Another explanatory variable is the total sentencing components ("the number of counts for a crime an individual is charged with and sentenced for. For example, an individual who breaks into someone's house can be simultaneously charged with breaking and entering and criminal trespass, as well as, potentially, violation of probation. Each of these individual charges can carry a separate sentence component that contributes to the total sentence length"). The other explanatory variables should be self-evident. For some reason, the authors do not report the intercept coefficient, but the coefficient estimates (with the standard errors in parentheses), are reported below. Dependent Variable: Natural Logarithm of Time Served, In(time served) Explanatory Variables Light skin Thin Total sentencing components Parole arrest Conviction date Homicide Robbery Habitual felon Total infractions in prison n R2 Coefficients and Standard Errors in Parentheses -0.109 (0.040) -0.099 (0.021) 0.057 (0.004) 0.674 (0.047) -0.001 (0.000) 1.496 (0.070) 0.764 (0.046) 1.973 (0.111) 0.053 (0.002) 11,093 0.280 How many of the explanatory variables are dummy variables? O 2 O 6 08 0 1 Question 19 3 pts Consider the multiple regression output from the question above regarding prison time. The 99-percent confidence interval for the coefficient on homicide is approximately: 01.196 to 1.796 1.359 to 1.633 O 1.426 to 1.546 O 1.316 to 1.676

Answer 1

Answer (20):

Here F-test will be used for chceking the overall significance of the model. The hypothesis is

H₀ : All the slope coefficients are zero i.e R² = 0

H₁ : One of the slope coefficients is not zero i.e. R² > 0

The test statistic for this test is F. The relationship between R² and F is given as:

F = [R²/(k-1)] / [(1-R²)/(n-k)] = [R²/(1-R²)] * [(n-k)/(k-1)]

Here, R² = 0.28, n = 11,093 and k = 9+1 = 10

So, F = 0.28/(1-0.28) * (11093-10)/(10-1)

F = (0.28/0.72) * (11083/9) = 0.3889 * 1231.4444 = 478.9087 ~ 479

Thus, the value of test statistic is approximately  479.

(question 21 not provided here)