Sign In
Not register? Register Now!
Essay Available:
Pages:
4 pages/≈1100 words
Sources:
Check Instructions
Style:
APA
Subject:
Mathematics & Economics
Type:
Math Problem
Language:
English (U.S.)
Document:
MS Word
Date:
Total cost:
$ 17.28
Topic:

Regression model, Model Coefficients, and Statistical Significance

Math Problem Instructions:

complete this exam with 4 questions

Time allowed: 3 hours Answer all questions. Marks for each indicated in square brackets. Question 1: [20 marks] Consider the following estimated regression results on a sample of 753 women: where the subscript i denotes the individual; hours is the annual hours of employed work; kidslt6 is the number of kids less than 6 years old; kidsge6 is the number of kids 6-18 years old; age is the woman’s age (in years); educ is the woman’s education (in years); and othfaminc is other family income (measured in thousands of dollars). The standard error for each estimated coefficient is listed in parentheses. (a) Interpret each of the estimated model’s coefficients and determine its statistical significance. (b) Are the signs (positive or negative) on each coefficient what you would expect to see? Explain. (c) Is the model statistically significant overall? Question 2: [5 marks] Consider the regression model: Explain in detail how you would test the following hypotheses: (a) (b) Question 3: [5 marks] Suppose that an individual’s wages depend positively on both their years of education and their ability. Years of education and ability are also positively correlated with each other. Ability, hoursi = 1346.75 (287.12) − 504.53 (63.96) ⋅ kidslt 6i − 82.49 (24.97) ⋅ kidsge6i −20.18 (4.54) ⋅ agei + 56.55 (13.94) ⋅ educi − 10.49 (2.71) ⋅ oth faminci R2 = 0.1180 F = 19.99 Prob > F = 0.0000 Yi = β0 + β1xi1 + β2xi2 + β3xi3 + ui H0 : β1 = β2 = 0 H0 : β1 = β2 however, is difficult to measure. The survey data you are using thus contain measures of only wages and years of education. Describe the consequences of running a regression model of wages (Y) on years of eduction (X) that omits ability from the model. Question 4: [10 marks] Suppose you have real estate sales data on price (in $), north (=1 if north location and =0 if south), and older (=1 if the house is 10 years of age or older; =0 if the house is less than 10 years old). (a) For the model , explain how you would interpret each coefficient. (b) Now modify the model in (a) to allow for the possibility that the effects of age differ by location. Explain how you would interpret each of this new model’s coefficients.

Math Problem Sample Content Preview:
TRENT UNIVERSITY DEPARTMENT OF ECONOMICS ECON-3200: ECONOMETRICS FINAL EXAM
DECEMBER 20, 2020
Time allowed: 3 hours
Answer all questions. Marks for each indicated in square brackets.

Question 1: [20 marks]

Consider the following estimated regression results on a sample of 753 women:

hours i = 1346.75 − 504.53 ⋅ kidslt 6i − 82.49 ⋅ kidsge6i

(287.12)

(63.96)

(24.97)

−20.18 ⋅ agei + 56.55 ⋅ educ − 10.49 ⋅ othfaminc

(4.54)

(13.94)

(2.71)

R2 = 0.1180

F = 19.99 Prob> F =0.0000

where the subscript i denotes the individual; hours is the annual hours of employed work; kidslt6 is the number of kids less than 6 years old; kidsge6 is the number of kids 6-18 years old; age is the woman’s age (in years); educ is the woman’s education (in years); and othfaminc is other family income (measured in thousands of dollars). The standard error for each estimated coefficient is listed in parentheses.

* Interpret each of the estimated model’s coefficients and determine its statistical significance.

13465.75 is the y-intercept

The standard error (S.E.) measures average deviation of the prediction errors about the regression line

The t statistic, t= coefficient / standard error = 1346.75 / 287.12= 4.6905

The p-value is < 0.00001 and the result is significant at p < 0.05.

* The annual hours of employed work decreases by 504.53 when the number of kids less than 6 years old increases by 1

The t statistic, t= coefficient / standard error 504.53/ 63.96

t=7.89

Degrees of freedom (DF is (number of observations minus the estimated parameters) =753-6= 747

The p-value is < .00001 (One-tailed) and the result is significant at p < 0.05.

* The annual hours of employed work decreases by 82.49 when the number of kids 6-18 years old increases by 1

t=82.49/ 24.97= 3.3

The p-value is 0.000501 (One-tailed) The result is significant at p < 0.05.

* The annual hours of employed work decreases by 20.18 when woman’s age (in years) increases by 1

t=20.18/ 4.54 = 4.44

The p-value is < 0.00001(One-tailed)The result is significant at p < 0.05.

* The annual hours of employed work increases by 56.55 when the woman’s education (in years) increases by 1

t=56.55 /13.94 =4.06

The p-value is 0.000028 (One-tailed) The result is significant at p < 0.05.

* The annual hours of employed work decreases by 10.49 when the family income (measured in thousands of dollars increases by 1

t=10.49/ 2.71 =3.8708

The p-value is 0.000059(One-tailed)The result is significant at p < 0.05

* Are the signs (positive or negative) on each coefficient what you would expect to see? Explain.

The number of kids less than 6 years old is a negative coefficient as expected as mothers with young children are more likely to spend time caring for them, and this implies less time working

The number of kids 6-18 years old is also a negative coefficient as mothers take more time cari...
Updated on
Get the Whole Paper!
Not exactly what you need?
Do you need a custom essay? Order right now:
Order

👀 Other Visitors are Viewing These APA Math Problem Samples:

HIRE A WRITER FROM $11.95 / PAGE
ORDER WITH 15% DISCOUNT!
Order Now