Exam 15: Inference With Regression Models

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

A sample of 200 monthly observations is used to run a simple linear regression: Returns = β₀ + β₁ Leverage + ε.A 5% level of significance is used to study if leverage has a significant influence on returns.The value of the test statistic for the regression coefficient of Leverage is calculated as t₁₉₈ = -1.09,with an associated p-value of 0.2770.The correct decision is to __________________________________________________________.

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 ______________.

A marketing analyst wants to examine the relationship between sales (in $1,000s)and advertising (in $100s)for firms in the food and beverage industry and so collects monthly data for 25 firms.He estimates the model: Sales = β₀ + β₁ Advertising + ε.The following table shows a portion of the regression results. When testing whether Advertising is significant at the 10% significance level,the conclusion is to _______________________________.

Serial correlation occurs when the error term is ______________________.

One of the assumptions of regression analysis is ___________________________________________________.

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 + β₁ Double 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. Excel shows that the 95% confidence interval for β₁ is [−0.12,−0.002].When determining whether or not Double Faults is significant at the 5% significance level,he ________________________________________________________.

The accompanying table shows the regression results when estimating y = β₀ + β₁x + ε. Is x significantly related to y at the 5% significance level?

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% confidence interval for E(y)when x equals 2? (Note that t_0,025,10 = 2.228. )

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

Conditional on x₁,x₂,... ,x_k,the error term ε is ________ distributed.

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 + β₁ Service + ε.The following table summarizes a portion of the regression results. Which of the hypotheses will determine whether the slope differs from zero?

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 marketing analyst wants to examine the relationship between sales (in $1,000s)and advertising (in $100s)for firms in the food and beverage industry and so collects monthly data for 25 firms.He estimates the model: Sales = β₀ + β₁ Advertising + ε.The following table shows a portion of the regression results. Which of the following are the competing hypotheses used to test whether Advertising is significant in predicting Sales?

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: __________________.

When testing r linear restrictions imposed on the model y = β₀ + β₁x₁ + ...+ β_kx_k + ε,the test statistic is assumed to follow the F(df₁,df₂)distribution with ____________________.

A wavelike movement in residuals suggests positive serial correlation.

A researcher analyzes the factors that may influence amusement park attendance.She estimates the following model: Attendance = β₀ + β₁ Price + β₂ Temperature + β₃ Rides + ε,whereAttendance is the daily attendance (in 1,000s),Price is the gate price (in $),Temperature is the average daily temperature (in ^oF),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 Temperature is significant at the 5% significance level,she ________________________________________________________________.

A researcher analyzes the factors that may influence amusement park attendance.She estimates the following model: Attendance = β₀ + β₁ Price + β₂ Temperature + β₃ Rides + ε,whereAttendance is the daily attendance (in 1,000s),Price is the gate price (in $),Temperature is the average daily temperature (in ^oF),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 Rides is significant at the 1% significance level,she ____________________________________________________________.

Multicollinearity is suspected when ________________________________________________.