0.9 The study of how a dependent variable y is related to two or more independent variables is called multiple linear regression. The mathematical equation relating the expected value of the dependent variable to the value of the independent variables, which has the form of y=B0+B1X1+B2X2+…+BqXq+e is called a multiple regression model. The process of making conjecture about the value of a population parameter, collecting sample data that can be used to assess this conjecture, measuring the strength of the evidence against the conjecture that is provided by the sample, and using these results to draw a conclusion about the conjecture is known as statistical inference. _____ refers to the use of sample data to calculate a range of values that is believed to include the unknown value of a population parameter. Hypothesis testing Suppose a residual plot of x verses the residuals, shows a non-constant variance. In particular, as the values of x increase, suppose that the value of the residuals also increase. This means that as the values of x get larger, the ability to predict y becomes less accurate. If GPA and Aptitude Test Scores are linearly related, which of the following must be true? The following data show the results of an aptitude test and the grade point average of 10 students. β ≠ 0
The tests of significance in regression analysis are based on assumptions about the error term ε . One such assumption is that the values of ε are independent. The tests of significance in regression analysis are based on assumptions about the error term ε. One such assumption is that the error term ε follows a ________ distribution for all values of x . Normal When we use the estimated regression equation to develop an interval that can be used to predict the mean for ALL units that meet a particular set of given criteria, that interval is called a confidence interval. When we use the estimated regression equation to develop an interval that can be used to predict the mean for a specific unit that meets a particular set of given criteria, that interval is called a prediction interval. The following regression model has been proposed to predict sales at a gas station where x1= their previous day’s sales (in $1000’s) x2= population within 5 miles (in 1000’s) x3= 1 if any form of advertising was used, 0 if otherwise, and sales (1000’s). Predict sales in dollars for a store with competitor’s previous day’s sales of 43,000 a population of 10,000 within 5 miles and twenty radio advertisements. $86,000 Does the t test indicate a significant relationship between GPA and Aptitude Test Score? State the test statistic, and then state your conclusion. Use ∝ = 0.05. The following data show the results of an aptitude test and the grade point average of 10 students. t = 6.25. The p -value is less than 0.05, so there is evidence is sufficient to conclude that a significant relationship exists between GPA and Aptitude Test Scores. This pie chart displays the age frequencies of students in a Business Analysis class. What percent of students are younger than 34 years old? 9% A variable used to model the effect of categorical independent variables is called a dummy variable.
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- Winter '10
- Regression Analysis, Wyche Accounting