Exam 15: Inference With Regression Models

________ plots can be used to detect common violations, and they can be used to detect outliers.

The accompanying table shows the regression results when estimating y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε. a. Specify the competing hypotheses to determine whether the explanatory variables are jointly significant. B) At the 5% significance level, are the explanatory variables jointly significant? Explain. C) At the 5% significance level, is x₂ significant in explaining y? Explain. D) At the 5% significance level, is the slope coefficient attached to x₃ different from −2?

In regression, multicollinearity is considered problematic when two or more explanatory variables are ________.

If in the multiple linear model the slope coefficient β_i is negative, it suggests an inverse (negative) relationship between the explanatory variable x_i and the response variable y holding the other explanatory variables constant.

An economist estimates the following model: y = β₀ + β₁x + ε. She would like to construct interval estimates for y when x equals 2. She estimates a modified model where y is the response variable and the explanatory variable is now defined as x^* = x - 2. A portion of the regression results is shown in the accompanying table. According to the modified model, which of the following is a 95% prediction interval for y when x equals 2? (Note that t_0.025,10 = 2.228.)

With the partial F test, we basically analyze the ratio of (SSE_R - SSE_U) to ________.

If the variance of the error term is not the same for all observations, we ________.

A sports analyst wants to exam the factors that may influence a tennis player's chances of winning. Over four tournaments, he collects data on 30 tennis players and estimates the following model: Win = β₀ + β₁Double Faults + β₂Aces + ε, where Win is the proportion of winning, Double Faults is the percentage of double faults made, and Aces is the number of aces. A portion of the regression results are shown in the accompanying table. When testing whether the explanatory variables jointly influence the response variable, the null hypothesis is ________.

Excel and virtually all other statistical packages report the p-value ________.

A sociologist estimates the regression relating Poverty (y) to Education (x₁). The estimated regression equation is: = 71.68 - 0.69x₁; n = 39; SSE = 152. In an attempt to improve the results, he adds two more explanatory variables: Median Income (x₂, in $1,000s) and the Mortality Rate (x₃, per 1,000 residents). The estimated regression equation is: = 59.80 - 0.44x₁- 0.18x₂ + 0.17x₃; n = 39; SSE = 60. A) Formulate the hypotheses to determine whether Median Income and the Mortality Rate are jointly significant in explaining Poverty. B) Calculate the value of the test statistic. C) At the 5% significance level, find the approximate value of the critical value(s). D) What is the conclusion to the test?

Tiffany & Co. has been the world's premier jeweler since 1837. The performance of Tiffany's stock is likely to be strongly influenced by the economy. Monthly data for Tiffany's risk-adjusted return and the risk-adjusted market return are collected for a five-year period (n = 60). The accompanying table shows the regression results when estimating the Capital Asset Pricing Model (CAPM) model for Tiffany's return. You would like to determine whether an investment in Tiffany's is riskier than the market. When conducting this test, you set up the following competing hypotheses: ________.

A researcher analyzes the factors that may influence amusement park attendance. She estimates the following model: Attendance = β₀ + β₁Price + β₂Temperature + β₃Rides + ε, where Attendance is the daily attendance (in 1,000s), Price is the gate price (in $), Temperature is the average daily temperature (in °F), and Rides is the number of rides at the amusement park. A portion of the regression results is shown in the accompanying table. When testing whether the explanatory variables Temperature and Rides are jointly significant, the error sum of squares for the restricted model is SSE_R = 12,343.78. Which of the following is the value of the test statistic when conducting this test?

A manager at a local bank analyzed the relationship between monthly salary (y, in $) and length of service (x, measured in months) for 30 employees. She estimates the following model: Salary = β₀ + β₁Service + ε. The following table summarizes a portion of the regression results. Which of the hypotheses will determine whether the slope differs from zero?

Consider the following regression results based on 30 observations. = 238.33 - 0.95x₁ + 7.13x₂ + 4.76x₃; SSE = 3,439 = 209.56 - 1.03x₁ + 5.24(x₂ + x₃); SSE = 3,559 A) Formulate the hypotheses to determine whether the influences of x₂ and x₃ differ in explaining y. B) Calculate the value of the test statistic. C) At the 5% significance level, find the critical value(s). D) What is your conclusion to the test?

If the residuals are correlated, then the residuals should show no pattern around the horizontal axis.

A manager at a local bank analyzed the relationship between monthly salary (y, in $) and length of service (x, measured in months) for 30 employees. She estimates the following model: Salary = β₀ + β₁Service + ε. The following table summarizes a portion of the regression results. Which of the following hypotheses will determine whether the intercept differs from zero?

A researcher analyzes the factors that may influence the poverty rate and estimates the following model: where y is the poverty rate (y, in %), is the percent of the population with at least a high school education, is the median income (in $1,000), and is the mortality rate (per 1,000 residents). The researcher would like to construct interval estimates for y when equal 85%, $50,000, and 10, respectively. The researcher estimates a modified model where poverty rate is the response variable and the explanatory variables are now defined as and . A portion of the regression resuts is shown in the accompanying table. A) According to the modified model, what is the point estimate for the poverty rate when and equal 85%, $50,000, and 10, respectivly. B) According to the modified model, what is a 95% confidence interval for the expected poverty rate when equal 85%, $50,000, and 10, respectively? C) According to the modified model,what is a 95% prediction interval for the poverty rate when equal 85%, 50,000, and 10, respectively?

Given the following portion of regression results, which of the following conclusions is true with regard to the F test at the 5% significance level?

A crucial assumption in a regression model is that the error term is not correlated with any of the explanatory variables.

Consider the following simple linear regression model: y = β₀ + β₁x + ε. When determining whether there is a negative linear relationship between x and y, the alternative hypothesis takes the form ________.