STAT 2225: Statistical Inference Quiz 5 & 6 Solutions and Analysis

This document contains the solutions to two quizzes (Quiz 5 and Quiz 6) from a STAT 2225 course, focusing on statistical inference. Quiz 5 covers regression analysis, including calculating the regression line, constructing an ANOVA table, and hypothesis testing related to the relationship between post-secondary education and annual income. Quiz 6 delves into multiple regression analysis, examining the relationship between credit card charges, income, and the number of persons in a household. The solution includes calculations for standard deviation, confidence intervals for regression coefficients, and interpretations of the results. It addresses questions on the number of households in the data, the calculation of the standard deviation of the dependent variable, and the construction and interpretation of a 90% confidence interval for the income regression coefficient. The analysis also covers the null hypothesis and its rejection based on the p-value.

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Question 1
a) The total number of households in the data is 43 or (42+1).
b) Standard deviation of y = Standard error * (number of households)0.5 = 421.083*(43)0.5 =
2721.226
c) The mean value associated with the variable income is 30.7207
Lower level of confidence interval = Mean – Margin of Error
Upper level of confidence interval = Mean + Margin of Error
Mean value of regression coefficient = 30.7207
Margin of Error = T stat* Standard Error
Standard error of regression coefficient= 4.76792
For df = (43-1) = 42, and 90% level of confidence, relevant t stat (two tail) = 1.68195
Lower level of confidence interval = 30.7207-1.68195*4.76792 = 22.7013
Higher level of confidence interval = 30.7207+1.68195*4.76792 = 38.7401
The 90% confidence interval for the income regression coefficient is (22.7013, 38.7401)
The above interval implies that there is a 90% chance that the mean regression coefficient for
income variable for the household population is expected to lie between 22.7013 and
38.7401.
d) The null hypothesis being tested is the all the regression coefficients can be assumed to
zero and thereby insignificant. This in turn would imply that the regression model is not
significant. Since the p value has come out to be zero, hence it would imply that null
hypothesis is rejected which would mean that regression model is significant as atleast one
slope coefficient is statistically significant.