Analyzing Regression Models and Statistical Tests: Assignment

This document provides a comprehensive solution to a statistics assignment focusing on regression analysis and hypothesis testing. The assignment covers a range of statistical concepts and techniques, including linear regression, t-statistics, p-values, F-statistics, and variance-covariance matrices. The solution details step-by-step instructions and explanations for each question, from interpreting coefficients and determining statistical significance to constructing point and interval estimates and performing hypothesis tests. The assignment involves the analysis of data using statistical software, requiring the application of various formulas and the interpretation of statistical outputs. The document also includes instructions on how to use statistical software to perform the analysis and interpret the results. The solutions provided are designed to guide students through the process of understanding and applying statistical methods to real-world problems. This assignment covers a wide range of topics within statistics, from basic regression models to more complex hypothesis testing and inference techniques.

Question A
Steps
a) Click Statistics > Linear models and related > Linear regression on the main menu,
b) You will be presented with the Regress – Linear regression dialogue box:
c) Select your Dependent variable: drop-down box, and your the Independent
variables: drop-down box
d) Click the button. This will generate the output.
Question B
A unit change in total expenditure leads to a XX% increase/decrease in WALC
A unit change in number of children leads to a XX unit increase/decrease in WALC
A unit change in age leads to a XX unit increase/decrease in WALC
Question C
For this question, you look at the P value for each of the coefficients, if the p value output is less than
0.05, then the coefficient is significant otherwise, it is not significant
Question D
For this question, you test the t statistic output for NK against the t value from the tables for 5%
significance level for the n-1 degrees of freedom in which N is the number of variables in the assignment
Question E
For this question, you first add another variable AGE squared by submitting the code generate AGE2 =
AGE^2
You then run the regression model again using steps in Question A but this time you also include the
new variable AGE2 as an independent variable
Question F
For this question use the command, matrix list e(V) to generate the variance covariance matrix
Question G

For the point estimate we use the mean value
For the interval estimate we use x +¿−ta
2
¿ to find interval a<x<b, the t is the t statistic in the output
Question H
For the point estimate we use the mean value
For the interval estimate we use x +¿−ta
2
¿ to find interval a<x<b the t is the t statistic in the output
Question I
For the point estimate we use the mean value
For the interval estimate we use x +¿−ta
2
¿ to find interval a<x<b, the t is the t statistic in the output
Question J
A summary could be a table showing the limits of the point and interval estimates
Question K
Use steps in question A to regress model this time without AGE and AGE2 as independent variables
Question L
We use the following as the test statistic
Where RSSR is the sum of squares of the new model and RSSF is the sum of squares of the previous
model and Where DfR is the degrees of freedom of the new model and DfF is the degrees of freedom of
the previous model
Degrees of freedom = number of variables -1

We then compare this value with the F value from the output
We reject the null hypothesis if f critical value is greater than the F calculated value
Question M
For this question, we use the output from part e and compare the p value of the NK, if the p value is less
than 0.5 we conclude that the variable NK is significant
Question N
In this case we use the formula x +¿−F a
2
¿ where F = t squared
We then compare the value from the F calculated with the F critical value at 5% significance level with
the number of variables - 2 as the degrees of freedom
We then rekject the null hypothesis s f critical is greater than F calculated value