Linear Regression. 1. The coefficient of determination of 0.94 for a regression

Question

Linear Regression. 1. The coefficient of determination of 0.94 for a regression analysis would indicate. A. 6% of the variation is explained by the regression equation. B. 94% of the variation is not explained by the regression equation. C. 94% of the variation is explained by the regression equation. D. 6% of the variation is random

2. Unlike regression, trend analysis limits the predictions of the unknown variable to historical levels of the same variable. T/F

3. A simple regression involves a single independent variable. T/F

4. A typing instructor builds a regression model to investigate what factors determine typing speed for students with two months of instruction. Her regression equation looks likes: Y’=7X2+5X2+3X+11 Where Y’= typing speed in words per minute; X3= hours of instruction per week; X2= hours of practice per week; X= hours of typing per week necessary for school or work; A new student is taking 2 hours of typing instruction per week, will practice 5 hours per week and must type 2.5 hours per week for work. If the standard error of the estimate is 4, within what range do we have a 94.45% probability that that students typing speed will be in two months. A. 53.5 and 61.5 WPM B. 49.5 and 65.5 WPM C. 57.5 and 65.5 WPM D. none of the above

5. In statistical terminology, an additional independent variable lowers the degrees of freedom. T/F

6. A study is being made of the relationship between seniority, I.e, years of service with the company, and the number of workdays absent per year. The following regression line is derived from the data: Days absent = 9.44 -1.09(years employed) The best estimate of the number of times a 5-year employee will be absent. A. 8.35 B. 3.99 C. 5.45 D. None of the above

7. An independent variable has a coefficient of 2.9 and a standard deviation of 0.8. what is the T-ratio, given to the third decimal place? A. 2.76 B. 3.625 C. .3625 D. none of the above

8. Which of the following is not an assumption for simple linear regression? A. The mean of each error component is zero B. Each error component follow an approximate normal distribution. C. The error components lie on a straight line. D. The variance for the error components is the same for each value of X.

9. Let us imagine that the number of automobile accidents in a certain region are related to the regional number of registered automobiles in the tens of thousands (b1), alcoholic beverage sales in $10,000(b2) and decrease in the price of gasoline in cents (b3). Furthermore, imagine that the regression formula has been calculated as : Y=a+b1X1+b2X2+b3X3 where Y= the number of automobile accidents, a=7.5, b1=3.5, b2=4.5 and b3=2.5. Calculate the expected number of automobile accidents for a football weekend if the region has 25,000 registered vehicles, $75,000 worth of beer is sold and a gas war causes a 10 cent drop in a gallon of gas. A. 75 B. 475 C. 45 D. 306

10. The coefficient of determination tells us how much variation in the data can be explained by the regression model. T/F

Explanation / Answer

3. A simple regression involves a single independent variable. True.

In simple linear regression, one predicts scores on one variable from the scores on a second variable. The variable we are predicting is called the criterion variable and is referred to as Y. The variable Y is dependent variable and the other is independent variable.

1. Coefficient of determination, r 2 , is a measure of how much of the variability in one variable can be "explained by" variation in the other. Thus, C. 94% of the variation is explained by the regression equation.

6.Days absent=9.44-1.09*5

=3.99

8.The following is not an assumption for simple linear regression:

D. The variance for the error components is the same for each value of X.

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