BIVARIATE LINEAR REGRESSION

Bivariate Linear Regression Analysis and Cumulative Knowledge Question Student Name Institution Professor Name Course Date Bivariate Linear Regression Analysis and Cumulative Knowledge Question Problem Set 1: Linear Regression Analysis Research Scenario: An admissions counselor wants to find out if TOEFL® scores are predictive of college GPA for international students at a local university. The TOEFL is the Test of English as a Foreign Language, which the school requires for admission, and students can score from 0-120, with 120 being a perfect score. The data from the latest freshmen class are in the table below. Can TOEFL scores be used as a predictor of college GPA?Using this table, enter the data into a new SPSS data file and run a linear regression analysis to test whether TOEFL scores predict college GPA. Create a scatterplot with a regression line to display the relationship between the variables. Remember to put your initials within any and all variable names. Follow the directions below the table to complete the homework.Problem Set 1: Linear Regression Analysis Research Scenario: An admissions counselor wants to find out if TOEFL® scores are predictive of college GPA for international students at a local university. The TOEFL is the Test of English as a Foreign Language, which the school requires for admission, and students can score from 0-120, with 120 being a perfect score. The data from the latest freshmen class are in the table below. Can TOEFL scores be used as a predictor of college GPA?Using this table, enter the data into a new SPSS data file and run a linear regression analysis to test whether TOEFL scores predict college GPA. Create a scatterplot with a regression line to display the relationship between the variables. Remember to put your initials within any and all variable names. Follow the directions below the table to complete the homework. TOEFL® Score College GPA 94 80 112 72 93 101 76 90 83 68 113 74 100 52 3.0 2.7 1.5 2.9 3.2 3.6 2.0 3.7 2.3 3.4 3.6 2.7 3.4 2.7 1 Paste SPSS output. (10 pts) Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .125a .016 -.066 .6698 a. Predictors: (Constant), TJP_Test of English as a Foreign Language Scores ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression .085 1 .085 .190 .671a Residual 5.384 12 .449 Total 5.469 13 a. Predictors: (Constant), TJP_Test of English as a Foreign Language Scores b. Dependent Variable: TJP_College GPA Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 2.505 .940 2.663 .021 TJP_Test of English as a Foreign Language Scores .005 .011 .125 .436 .671 a. Dependent Variable: TJP_College GPA 2 Write an APA-style Results section based on your analysis. Include your scatterplot as an APA-style Figure, with figure number and title, as demonstrated in the Results Section presentation. (Results = 12 pts; Figure = 8 pts) Results Whether TOEFL Scores Predict College GPA From the above linear regression analysis model summary, r = 0.125, showing a weak positive linear relationship between TOEFL scores and College GPA. The adjusted r2 = -0.066, indicating that the TOEFL scores can explain -6.6% of the total variation in the College GPA. From the ANOVA table, p = 0.671, which is more than the 0.05 significance level, suggesting that the regression equation/ TOEFL scores (independent variable) do not significantly predict College GPA (dependent variable). The regression equation, Y = B0 +B1X, can be found using the information from the coefficients table above. The equation is Y = 2.505 +0.005X; therefore, College GPA= 2.505 +0.005 TOEFL scores. Decision about the Null Hypothesis The hypotheses for this linear regression analysis are as follows. H0: There is no effect of the TOEFL scores on the College GPA. H1: There is an effect of the TOEFL scores on the College GPA. Problem Set 2: Linear Regression AnalysisResearch Scenario: A social psychologis...