Homework Answers
Basic Calculations: we have to calculate the t-values for each problem. then we have to look up for the p-value using t table.
and taking degrees of freedom as (n-2). here n is sample size.
1) beta coefficient = -0.1748, standard error = 0.1840
t value = (-0.1748/0.1840) = -0.95 now use DF = n-2 = 946-2 = 944
so we get: P value= 0.1712 (at 5% significance level)
2) beta coefficient = 0.24462, standard error = 0.1620
t value = (0.24462/0.1620) = 1.51 , DF = n-2 = 946-2 = 944
so we get: P value= 0.0657 (at 5% significance level)
3) beta coefficient = 0.03346, standard error = 0.1020
t value = (0.03346/0.1020) = 0.328 , DF = n-2 = 946-2 = 944
so we get: P value= 0.3715 (at 5% significance level)
4) beta coefficient = 0.05822, standard error = 0.1420
t value = (0.05822/0.1420) = 0.41 , DF = n-2 = 946-2 = 944
so we get: P value= 0.3410 (at 5% significance level)
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We consider the regression model Y=Bo + B1X + u sample size of n =946 And...
We consider the regression model Y = Bo + BiX + u And we found for...
We consider the regression model Y = Bo + BiX + u And we found for a sample size of n = 946 Û = 1.935 + 1.92 (-0.5429) (0.6100) Give the p-value for the test Ho:B1 = 0 Hl:B170 (round your answer to 3 digits after the decimal).
QUESTION 1 We consider the regression model Y= Bo+B1X u And we found for a sample...
QUESTION 1 We consider the regression model Y= Bo+B1X u And we found for a sample size of n 974 B1 -0.095 and S 0.02 Does X has a significant effect on Y at the 5 % level? True False
Consider the regression equation Y = Bo+B1Xi+u; where E[u;|Xi]=0 for all i = 1, ..., n....
Consider the regression equation Y = Bo+B1Xi+u; where E[u;|Xi]=0 for all i = 1, ..., n. Let B 1 be the OLS estimator for B 1. Which statement is the most irrelevant to the consistency of B1? Hint: see Lecture Note 2 (p.25-p.28) a. When n is large, the estimator B 1 is near the population parameter B1 O". Consistency of B1 is mathematically written as B1-B1 VB) is inversely proportional to the sample size n. Od. RMSE is close...
Suppose we fit the simple linear regression model (with the usual assumptions) Y = Bo+B1X+ €...
Suppose we fit the simple linear regression model (with the usual assumptions) Y = Bo+B1X+ € and get the estimated regression model ♡ = bo+bix What aspect or characteristic of the distribution of Y does o estimate? the value of Y for a given value of X the total variability in Y that is explained by X the population mean number of Y values above the mean of Y when X = 0 the increase in the mean of Y...
Consider the regression model: Y = Bo + B,X+u Which of the following assumptions would, if...
Consider the regression model: Y = Bo + B,X+u Which of the following assumptions would, if not satisfied, lead to a biased estimate of Bo and B? OE(u|X)=0 o untok- var (44)=o?, for all i Ou~ N(0,0%)
Exercise 4.11 Consider the regression model Y Po PX+u Suppose that you know Bo 1. Derive...
Exercise 4.11 Consider the regression model Y Po PX+u Suppose that you know Bo 1. Derive the formula for the least squares estimator of p The least squares objective function is OA. n (v2-bo-bx?) i-1 Ов. O B. n (M-bo-bX) /# 1 n Click to select your answer and then click Check Answer. Exercise 4.11 OA n Σ (--B,χ?) O B. E (Y-bo-b,X)2 j= 1 n Σ (Υ-Βo-bΧ) 3. j= 1 D. n Σ (Υ-0-b,) i- 1 Click to select...
QUESTION 1 Consider the following OLS regression line (or sample regression function): wage =-2.10+ 0.50 educ...
QUESTION 1 Consider the following OLS regression line (or sample regression function): wage =-2.10+ 0.50 educ (1), where wage is hourly wage, measured in dollars, and educ years of formal education. According to (1), a person with no education has a predicted hourly wage of [wagehat] dollars. (NOTE: Write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading minus sign symbol, a leading zero and trailing...
A simple linear regression model is given as follows Yi = Bo + B1Xi+ €i, for...
A simple linear regression model is given as follows Yi = Bo + B1Xi+ €i, for i = 1, ...,n, where are i.i.d. following N (0, o2) distribution. It is known that x4 n, and x = 0, otherwise. Denote by n2 = n - ni, Ji = 1 yi, and j2 = 1 1. for i = 1, ... ,n1 < n2 Lizn1+1 Yi. n1 Zi=1 1. Find the least squares estimators of Bo and 31, in terms of...
Type or pas 2. Let the population regression model between a dependent variable y and an...
Type or pas
2. Let the population regression model between a dependent variable y and an independent variable is given by y= Bo+ B1 x x+ u Suppose that E(u|x) = E(u) = 0 and V(ux) = o2. Based on a random sample ((y, ) i = 1,2,...n) of size n such that (xi- )2>0, let Bo and B be the OLS estimates of Bo and Bi respectively. Answer the following questions (c) Let B i Show that if B1...
Using the appropriate model, sample size n, and output: Model: Sample: n=8 S=.5561, = 93.1%...
Using the appropriate model, sample size n, and output:
Model:
Sample: n=8 S=.5561,
= 93.1% ,
adj = 90.3%
1. Report SSE,
, and s as shown on the output. Calculate
from SSE and other numbers. Report the total variation,
unexplained variation, and explained variation as shown on the
output. (Round answers to 4 decimal places.)
2. Report
and adjusted
as shown on the output. Calculate the F statistic. (Round your
answer to 3 decimal places.)
3. Find the...
We consider the regression model Y = Bo + BiX + u And we found for a sample size of n = 946 Û = 1.935 + 1.92 (-0.5429) (0.6100) Give the p-value for the test Ho:B1 = 0 Hl:B170 (round your answer to 3 digits after the decimal).
QUESTION 1 We consider the regression model Y= Bo+B1X u And we found for a sample size of n 974 B1 -0.095 and S 0.02 Does X has a significant effect on Y at the 5 % level? True False
Consider the regression equation Y = Bo+B1Xi+u; where E[u;|Xi]=0 for all i = 1, ..., n. Let B 1 be the OLS estimator for B 1. Which statement is the most irrelevant to the consistency of B1? Hint: see Lecture Note 2 (p.25-p.28) a. When n is large, the estimator B 1 is near the population parameter B1 O". Consistency of B1 is mathematically written as B1-B1 VB) is inversely proportional to the sample size n. Od. RMSE is close...
Suppose we fit the simple linear regression model (with the usual assumptions) Y = Bo+B1X+ € and get the estimated regression model ♡ = bo+bix What aspect or characteristic of the distribution of Y does o estimate? the value of Y for a given value of X the total variability in Y that is explained by X the population mean number of Y values above the mean of Y when X = 0 the increase in the mean of Y...
Consider the regression model: Y = Bo + B,X+u Which of the following assumptions would, if not satisfied, lead to a biased estimate of Bo and B? OE(u|X)=0 o untok- var (44)=o?, for all i Ou~ N(0,0%)
Exercise 4.11 Consider the regression model Y Po PX+u Suppose that you know Bo 1. Derive the formula for the least squares estimator of p The least squares objective function is OA. n (v2-bo-bx?) i-1 Ов. O B. n (M-bo-bX) /# 1 n Click to select your answer and then click Check Answer. Exercise 4.11 OA n Σ (--B,χ?) O B. E (Y-bo-b,X)2 j= 1 n Σ (Υ-Βo-bΧ) 3. j= 1 D. n Σ (Υ-0-b,) i- 1 Click to select...
QUESTION 1 Consider the following OLS regression line (or sample regression function): wage =-2.10+ 0.50 educ (1), where wage is hourly wage, measured in dollars, and educ years of formal education. According to (1), a person with no education has a predicted hourly wage of [wagehat] dollars. (NOTE: Write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading minus sign symbol, a leading zero and trailing...
A simple linear regression model is given as follows Yi = Bo + B1Xi+ €i, for i = 1, ...,n, where are i.i.d. following N (0, o2) distribution. It is known that x4 n, and x = 0, otherwise. Denote by n2 = n - ni, Ji = 1 yi, and j2 = 1 1. for i = 1, ... ,n1 < n2 Lizn1+1 Yi. n1 Zi=1 1. Find the least squares estimators of Bo and 31, in terms of...
Type or pas
2. Let the population regression model between a dependent variable y and an independent variable is given by y= Bo+ B1 x x+ u Suppose that E(u|x) = E(u) = 0 and V(ux) = o2. Based on a random sample ((y, ) i = 1,2,...n) of size n such that (xi- )2>0, let Bo and B be the OLS estimates of Bo and Bi respectively. Answer the following questions (c) Let B i Show that if B1...
Using the appropriate model, sample size n, and output:
Model:
Sample: n=8 S=.5561,
= 93.1% ,
adj = 90.3%
1. Report SSE,
, and s as shown on the output. Calculate
from SSE and other numbers. Report the total variation,
unexplained variation, and explained variation as shown on the
output. (Round answers to 4 decimal places.)
2. Report
and adjusted
as shown on the output. Calculate the F statistic. (Round your
answer to 3 decimal places.)
3. Find the...
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