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Simple Linear Regression Assignment 1

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Simple Linear Regression Assignment 1. Which is the predictor variable (X) and which is the criterion variable (Y): • A military officer tests whether the duration of an overseas tour can predict the morale among troops overseas. 2. In each of the following, indicate the slope, the intercept, and explain how much the criterion variable (Y) changes as the predictor variable increases: a. Y = 2.10X + 10 b. Y = -3.14X +12 3. The researcher reports the following for the relationship between income and height among men: An analysis of the linear model showed a positive linear relationship, Y = 2.10X + 0.80, indicating that the height of men predicts income. a. Based on this description, what is the predictor variable (X)? b. Describe the direction of this relationship in words. 4. A researcher reports the following regression equation for the relationship between two variables: Y = 1.30X + 2. Find the predicted value of Y, given that X = 0, 2, 4, and 8. 5. There appears to be some evidence suggesting that early retirement may lead to memory decline (Rohwedder & Willis, 2010). The researchers gave a memory test to men and women aged 60 – 64 in several countries that have different retirement ages. For each country, the researchers recorded the average memory scores and the percentage of individuals in the 60-64 range who were retired. Note that a higher percentage retired indicates a younger retirement age for that country. The following data are similar to the results from the study. a. What is the predictor variable (X)? What is the outcome variable (Y)? b. Compute the regression equation BY HAND. Note: you will get NO CREDIT if you use a program to do anything more than be a calculator (as we have been saying ALL SEMESTER LONG) Country Sweden U.S.A. England Germany Spain Netherlands Italy France Belgium Austria Memory Score 9.3 10.9 10.7 9.1 6.4 9.1 7.2 7.9 8.5 9.0 % Retired 39 48 59 70 74 78 81 87 88 91 6. A team of clinical psychologists tested the extent to which levels of cognitive functioning were related to the number of symptoms for some disorder expressed in 15 patients. The researchers recorded the following values: SP = 48.60, SSx = 355.73, SSy = 96.40. a. What is the proportion of variance, r2, in symptoms (Y) that can be explained by levels of cognitive functioning (X)? b. If the total variation in Y is 96.40 (SSy = 96.40), then what is the SSregression (the amount of variation that is predicted by X)? c. What is the SSresidual (the amount of variation in Y that is remaining)? 7. A researcher tested whether time of day could predict mood in a sample of 14 college students. If SSresidual = 108, then what is the standard error of the estimate in this sample? 8. An analysis of regression measures the variability of which variable: X or Y? 9. A health psychologist hypothesizes that students who study more also exercise less because they spend so much time studying. She measures whether the number of hours (per week) spent studying could predict the number of hours exercising in a sample of 62 students. Complete the following regression table for this hypothetical study and make a decision to reject or not reject the null hypothesis. Source of Variation Regression Residual (error) Total SS df MS 80 Fobt 1440 Decision: 10. Chen, Dai, and Dong (2008) measured the relationship between scores on a revised version of the Aitken Procrastination Inventory (API) and actual procrastination among college students. Higher scores on the API indicate greater procrastination. They found that procrastination (Y) among college students could be predicted by API scores (X) using the following regression equation: Y-hat = 0.146X – 2.922. Estimate procrastination when: a. X = 30 b. X = 40 c. X = 50 11. A professor obtains SAT scores and freshman grade point averages (GPAs) for a group of n = 15 college students. The SAT scores have a mean of M = 580 with SS = 22,400 and the GPAs have a mean of 3.10 with SS = 1.26, and SP = 84. a. Find the regression equation for predicting GPA from SAT scores b. What percentage of the variance in GPAs is accounted for by the regression equation? c. Does the regression equation account for a significant portion of the variance in GPA? Use alpha = .05 to evaluate the F-ratio. 12. The figure below is a scatterplot of the life expectancy for females and the birthrate per 1000 population for 15 countries. a. b. c. d. e. f. g. h. i. j. k. Does this figure have a positive or negative slope? Explain. What is the value of the correlation coefficient between life expectancy for females and birthrate? Is this relationship significant? Explain. What is the proportion of variance explained by the model? Explain the pattern described in the figure. What is the value of the intercept? What is the value of the slope? What is the equation of the line for this relationship? What is the predicted life expectancy for women in a country with a birthrate of 10? What is the predicted life expectancy for women in a country with a birthrate of 11? What is the difference between the life expectancies predicted in (f) and (g)?