PSYC_2022A_LEC_11_TUTORIAL

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Regression TUTORIAL RACHEL RABI, PhD
TEST YOURSELF! Research Question: Do the number of hours of sleep a parent gets (X 1 ) and the number of hours of sleep their baby gets (X 2 ) predict how grumpy the parent is? Alpha level: α = .05 Takeaway Question: What is the regression equation? Hint : The numbers are taken from the “Estimate” column of the Model Coefficients table above.
TEST YOURSELF! Research Question: Do the number of hours of sleep a parent gets (X 1 ) and the number of hours of sleep their baby gets (X 2 ) predict how grumpy the parent is? Alpha level: α = .05 Takeaway Question: What is the regression equation? Hint : The numbers are taken from the “Estimate” column of the Model Coefficients table above. Ŷ This equation allows us to calculated Ŷ for any value of X 1 and X 2 in range of observed data
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Research Question: Do the number of hours of sleep a parent gets (X 1 ) and the number of hours of sleep their baby gets (X 2 ) predict how grumpy the parent is? Alpha level: α = .05 Ŷ Using the following regression equation, what is the predicted value (Ŷ) for parents’ grumpiness if the parent got 6 hours of sleep (X 1 ) and the baby got 8 hours of sleep (X 2 )? a) 179.75 b) 72.35 c) 54.43 d) I don’t know TEST YOURSELF!
Research Question: Do the number of hours of sleep a parent gets (X 1 ) and the number of hours of sleep their baby gets (X 2 ) predict how grumpy the parent is? Alpha level: α = .05 Ŷ Using the following regression equation, what is the predicted value (Ŷ) for parents’ grumpiness if the parent got 6 hours of sleep (X 1 ) and the baby got 8 hours of sleep (X 2 )? a) 179.75 b) 72.35 c) 54.43 d) I don’t know TEST YOURSELF! Ŷ Ŷ Ŷ If parent got 6 hours of sleep and baby got 8 hours of sleep the predicted level of parent grumpiness is 72.35. Ŷ
TEST YOURSELF! Research Question: Do the number of hours of sleep a parent gets (X 1 ) and the number of hours of sleep their baby gets (X 2 ) predict how grumpy the parent is? Alpha level: α = .05 Ŷ Using the following regression equation, what is the predicted value (Ŷ) for parents’ grumpiness if the parent got 3 hours of sleep (X 1 ) and the baby got 4 hours of sleep (X 2 )? a) 99.16 b) 152.86 c) 90.2 d) I don’t know
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TEST YOURSELF! Research Question: Do the number of hours of sleep a parent gets (X 1 ) and the number of hours of sleep their baby gets (X 2 ) predict how grumpy the parent is? Alpha level: α = .05 Ŷ Using the following regression equation, what is the predicted value (Ŷ) for parents’ grumpiness if the parent got 3 hours of sleep (X 1 ) and the baby got 4 hours of sleep (X 2 )? a) 99.16 b) 152.86 c) 90.2 d) I don’t know Ŷ Ŷ Ŷ If parent got 3 hours of sleep and baby got 4 hours of sleep the predicted level of parent grumpiness is 99.16.
Multiple linear regression allows the researcher to: a) determine the relationships among four or more variables. b) predict an individual's score on a dependent variable (outcome variable) from their scores on multiple independent or predictor variables. c) predict an individual's score on a dependent variable (outcome variable) from their score on the independent or predictor variable. d) infer the direction of causal relations. TEST YOURSELF!
Multiple linear regression allows the researcher to: a) determine the relationships among four or more variables. b) predict an individual's score on a dependent variable (outcome variable) from their scores on multiple independent or predictor variables. c) predict an individual's score on a dependent variable (outcome variable) from their score on the independent or predictor variable. d) infer the direction of causal relations. TEST YOURSELF!
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If there is a negative correlation between X and Y, then in the regression equation, Ŷ = b X + b 0 , ____. a) b > 0 b) b < 0 c) b 0 > 0 d) b 0 < 0 TEST YOURSELF!
If there is a negative correlation between X and Y, then in the regression equation, Ŷ = b X + b 0 , ____. a) b > 0 b) b < 0 c) b 0 > 0 d) b 0 < 0 TEST YOURSELF! b is the slope of the line (i.e., determines how much Y changes when X is increased by 1 unit) same direction as r b 0 is the Y-intercept (i.e., the value of Y when X = 0)
If there is zero correlation ( r = 0) between two variables, the line defined by the regression equation for these variables would be a _______. a) vertical line b) horizontal line c) curved line d) diagonal line TEST YOURSELF!
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If there is zero correlation ( r = 0) between two variables, the line defined by the regression equation for these variables would be a _______. a) vertical line b) horizontal line c) curved line d) diagonal line TEST YOURSELF! If no correlation btwn variable (r = 0) regression line will be a flat horizontal line Remember : slope of regression line in simple linear regression is directly analogous to the interpretation of our correlation
Practice Problem 1 Your roommate is convinced that it is possible to determine a person’s age based on the number of movies the person sees annually. a) What would be the dependent/outcome variable in this analysis? b) What would be the independent/predictor variable in this analysis? c) What type of analysis would your roommate perform to test this idea?
Practice Problem 1 Your roommate is convinced that it is possible to determine a person’s age based on the number of movies the person sees annually. a) What would be the dependent/outcome variable in this analysis? Person’s age b) What would be the independent/predictor variable in this analysis? # movies a person sees c) What type of analysis would your roommate perform to test this idea? Simple linear regression
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Your roommate is convinced that it is possible to determine a person’s age based on the number of movies the person sees annually. To test this idea your roommate collects data from a sample of people for whom the average age is 44 and the average number of movies watched per week is 2.5 . The regression equation for predicting a person’s age from the number of movies the person sees in a week was Ŷ = 0(X) + 44. a) What is the intercept? b) What is the slope? c) If X = 3, what is the predicted value of Y (i.e., the predicted age)? d) What does the slope tell us about the relationship between the two variables? Practice Problem 2
Your roommate is convinced that it is possible to determine a person’s age based on the number of movies the person sees annually. To test this idea your roommate collects data from a sample of people for whom the average age is 44 and the average number of movies watched per week is 2.5 . The regression equation for predicting a person’s age from the number of movies the person sees in a week was Ŷ = 0(X) + 44. a) What is the intercept? b 0 = 44 b) What is the slope? b = 0 c) If X = 3, what is the predicted value of Y (i.e., the predicted age)? Ŷ = 44 d) What does the slope tell us about the relationship between the two variables? It tells us that there is no relationship between the two variables Practice Problem 2
Your Turn: jamovi Practice Problem 1 Regression Try it out yourself! A university administrator wants to understand the best predictor of undergraduate student performance (cumulative GPA). They note the high school averages, math scores on an entrance exam, and verbal scores on an entrance exam, as well as the cumulative GPA of 224 graduating students. Use the data file “ College Success.csv ” to answer the following questions: 1) What is a research question that could be answered using these data? 2) Run a linear regression in jamovi and formulate the regression equation by hand
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Your Turn: jamovi Practice Problem 1 Regression Try it out yourself! A university administrator wants to understand the best predictor of undergraduate student performance (cumulative GPA). They note the high school averages, math scores on an entrance exam, and verbal scores on an entrance exam, as well as the cumulative GPA of 224 graduating students. Use the data file “ College Success.csv ” to answer the following questions: 1) What is a research question that could be answered using these data? Research Question: Do high school average, math entrance exam scores, and verbal entrance exam scores predict undergraduate student performance?
First step of multiple linear regression is to confirm there is a significant linear relationship between your predictors (X 1 , X 2 , etc.) and your outcome (Y) No significant linear relationship between verbal entrance exam scores and GPA should not include this predictor in the regression Your Turn: jamovi Practice Problem 1 Regression Try it out yourself!
Research Question: Are high school averages, math entrance exam scores, and verbal entrance exam scores predictive of undergraduate student performance? Alpha level: α = .05 Your Turn: jamovi Practice Problem 1 Regression Try it out yourself! What is the regression equation? Ŷ = . 𝟐𝟐 𝑿 𝟏 + . 𝟎𝟎𝟏 𝑿 𝟐 + . 𝟏𝟒
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Students applying to graduate school may be asked to take an admissions test. To study how well these predict performance in grad school, one study hypothesized a positive relationship between scores on the Graduate Management Admissions Test (GMAT) and performance in a graduate MBA program such that higher GMAT scores are associated with higher levels of academic performance (Ahmadi, Raiszadeh, & Helms, 1997). To test their hypothesis the researchers obtained the GMAT scores (range: 200 to 800) and GPA (range 0.00 to 4.00) from transcripts of students in an MBA program. These data can be found in GMAT_GPA.csv a) What is the dependent/outcome variable? b) What is the independent/predictor variable? c) What type of analysis would you conduct? d) What is a research question you can answer with these data? e) Conduct the analysis in jamovi and write an APA formatted conclusion. jamovi Practice Problem 2
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a) What is the dependent/outcome variable? performance in graduate school (GPA) b) What is the independent/predictor variable? performance on entrance test (GMAT scores) c) What type of analysis would you conduct? simple linear regression d) What is a research question you can answer with these data? Is performance on an entrance test a predictor of performance in graduate school? jamovi Practice Problem 2
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e) Conduct the analysis in jamovi and write an APA formatted conclusion. jamovi Practice Problem 2
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jamovi Practice Problem 3 A professor wants to know if class attendance and students’ expected performance predict student actual performance in a statistics course. They track how many lectures 30 students attend throughout the semester, ask them at the beginning of the year what final grade they expect to achieve, and record students’ final grades in the course at the end of the semester. These data can be found in “ Go To Class.csv ” a) What is the dependent/outcome variable? b) What is/are the independent/predictor variable(s)? c) What type of analysis would you conduct? d) What is a research question you can answer with these data? e) Conduct the analysis in jamovi and write an APA formatted conclusion
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jamovi Practice Problem 3 a) What is the dependent/outcome variable? Final grade b) What is/are the independent/predictor variable(s)? Expected performance, classes attended c) What type of analysis would you conduct? Multiple linear regression d) What is a research question you can answer with these data? Do expected performance and number of classes attended predict students’ grades in a statistics course?
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jamovi Practice Problem 3 e) Conduct the analysis in jamovi and write an APA formatted conclusion
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jamovi Practice Problem 3 A multiple linear regression analysis was conducted to examine if expected performance and class attendance predict final grades in a stats course. An initial examination identified a strong, positive, linear relationships between expected performance and final grade ( r = .79, p < .001), a moderate positive linear relationship between classes attended and final grade ( r = .525, p = .003) as well as a moderate positive relationship between classes attended and expected performance ( r = .396, p = .03). The regression results indicate that the overall model fit was good, F (2, 27) = 28.4, p < .001 with R 2 = .678, suggesting that 67.8% of the variability in final grade can be explained by the predictors. Specifically, attending more classes ( b = 1.43, t (27) = 2.12, p = .044) and expecting a higher grade ( b = 1.05, t (27) = 5.80, p < .001) each predicted higher final grades in the course.
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