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Revised 6-30-20 Multiple Regression Write-up (Graded Assignment) Username: Name Instructions: For this graded assignment, you will complete the write-up below after completing the corresponding tutorial to this assignment. You will delete figures and tables where appropriate and then insert correct figures and tables. Also delete and then insert correct answers where there is RED text. To begin, cut and paste the data set below into SPSS (or you can type in the data manually). Do not copy the header row when you paste into SPSS. Before carrying out the analysis in SPSS, you need to set up your data file correctly using the “Variable View” tab. Scenario: The purpose of this study was to see if students’ perceived enjoyment and value of learning can predict their GPA. Code Name Enjoyment Value GPA 1 Noah 72 91 3.3 2 Christian 78 78 3.8 3 Elijah 78 89 2.6 4 Nadia 79 85 2.2 5 Celia 88 90 3.6 6 Payton 71 82 2.8 7 Caroline 78 82 3.4 8 Lily 98 92 3.9 9 Madison 70 79 2.2 10 Macy 82 89 3.8 11 Shelby 67 71 2.2 12 Isaiah 76 85 3.1 13 Elliana 89 98 4.0 14 Allyson 80 70 2.5 15 Ada 78 87 3.5 16 Michael 68 99 3.7 FINDINGS Overview The purpose of this study was to see if students’ perceived enjoyment and value of learning could predict their grade point average (GPA). The predictor variables were enjoyment and value of learning. The criterion variable was GPA. A multiple regression was used to test the hypothesis. The Findings section includes the research question, null hypothesis, data screening, descriptive statistics, assumption testing, and results. Research Question RQ: Is there a significant predictive relationship between the criterion variable (GPA) and the linear combination of predictor variables (enjoyment and value of learning) for high school students? Null Hypothesis H0: There is no significant predictive relationship between the criterion variable (GPA) and the linear combination of predictor variables (enjoyment and value of learning) for high school students. Data Screening The researcher sorted the data and scanned for inconsistencies on each variable. No data errors or inconsistencies were identified. A matrix scatter plot was used to detect bivariate outliers between each the predictor variable, other predictor variables, and the criterion variable. No bivariate outliers where identified. See Figure 1 for the matrix scatter plots. Figure 1 Matrix Scatter Plots Descriptive Statistics Descriptive statistics were obtained on each of the variables. The sample consisted of 00 participants. Perceived learning is highly related to Expectancy Value Theory which consist of enjoyment and value. Scores on the perceived learning scales for enjoyment and value range from 50 to 100. A high score of 100 means that the student was very motivated about learning, whereas a low score of 50 means that the student had little motivation. GPA was based on a four-point grading scale. Descriptive statistics can be found in Table 1. Table 1 Descriptive Statistics Assumption Testing Assumption of Linearity The multiple regression requires that the assumption of linearity be met. Linearity was examined using a scatter plot. The assumption of linearity was met/not met. See Figure 1 for the matrix scatter plot. Assumption of Bivariate Normal Distribution The multiple regression requires that the assumption of bivariate normal distribution be met. The assumption of bivariate normal distribution was examined using a scatter plot. The assumption of bivariate normal distribution was met/not met. See Figure 1 for the matrix scatter plot. Assumption of Multicollinearity A Variance Inflation Factor (VIF) test was conducted to assure the absence of multicollinearity. This test was run because if a predictor variable (x) is highly correlated with another predictor variable (x), they essentially provide the same information about the criterion variable. If the Variance Inflation Factor (VIF) is too high (greater than 10), then multicollinearity is present. Acceptable values are between 1 and 5. The absence of multicollinearity was met/not met between the variables in this study. See Table 2 collinearity statistics. Table 2 Collinearity Statistics Results A multiple regression was conducted to see if there was a predictive relationship between the criterion variable (GPA) and the linear combination of predictor variables (enjoyment and value of learning) for high school students. The predictor variables were enjoyment and value of learning. The criterion variable was GPA. The researcher rejected/failed to reject the null hypothesis at the 95% confidence level where F(0, 00) = 00.00, p = .00. There was/was not a statistical relationship between the predictor variables and the criterion variable. See Table 3 for regression model results. Table 3 Regression Model Results The model’s effect size was extremely large/ very large/ large/ medium/ small where R = .000. Furthermore, R2 = .000 indicating that approximately 00% of the variance of criterion variable can be explained by the linear combination of predictor variables. See Table 4 for model summary. Table 4 Model Summary Because the researcher rejected/failed to reject the null, further analysis of the coefficients was/was not required. Based on the coefficients, it was found that the enjoyment/value was the best predictor of GPA where p = .00. See Table 5 for coefficients. Table 5 Coefficients Write-Up: Multiple Regression Instructions and Template Username: Instructions: For this graded assignment, you will complete the write-up below after completing the corresponding tutorial to this assignment. You will delete figures and tables where appropriate and then insert correct figures and tables. Also delete and then insert correct answers where there is RED text. To begin, cut and paste the data set below into SPSS (or you can type in the data manually). Do not copy the header row when you paste into SPSS. Before carrying out the analysis in SPSS, you need to set up your data file correctly using the “Variable View” tab. Scenario: The purpose of this study was to see if students’ perceived enjoyment and value of learning can predict their GPA. Code Name Enjoyment Value GPA 1 Noah 72 91 3.3 2 Christian 78 78 3.8 3 Elijah 78 89 2.6 4 Nadia 79 85 2.2 5 Celia 88 90 3.6 6 Payton 71 82 2.8 7 Caroline 78 82 3.4 8 Lily 98 92 3.9 9 Madison 70 79 2.2 10 Macy 82 89 3.8 11 Shelby 67 71 2.2 12 Isaiah 76 85 3.1 13 Elliana 89 98 4.0 14 Allyson 80 70 2.5 15 Ada 78 87 3.5 16 Michael 68 99 3.7 FINDINGS Overview The purpose of this study was to see if students’ perceived enjoyment and value of learning could predict their grade point average (GPA). The predictor variables were enjoyment and value of learning. The criterion variable was GPA. A multiple regression was used to test the hypothesis. The Findings section includes the research question, null hypothesis, data screening, descriptive statistics, assumption testing, and results. Research Question RQ: Is there a significant predictive relationship between the criterion variable (GPA) and the linear combination of predictor variables (enjoyment and value of learning) for high school students? Null Hypothesis H0: There is no significant predictive relationship between the criterion variable (GPA) and the linear combination of predictor variables (enjoyment and value of learning) for high school students. Data Screening The researcher sorted the data and scanned for inconsistencies on each variable. No data errors or inconsistencies were identified. A matrix scatter plot was used to detect bivariate outliers between each the predictor variable, other predictor variables, and the criterion variable. No bivariate outliers were identified. See Figure 1 for the matrix scatter plots. Figure 1. Matrix scatter plot. Descriptive Statistics Descriptive statistics were obtained on each of the variables. The sample consisted of 16 participants. Perceived learning is highly related to Expectancy Value Theory which consist of enjoyment and value. Scores on the perceived learning scales for enjoyment and value range from 50 to 100. A high score of 100 means that the student was very motivated about learning, whereas a low score of 50 means that the student had little motivation. GPA was based on a four-point grading scale. Descriptive statistics can be found in Table 1. Table 1 Descriptive Statistics Descriptive Statistics N Minimum Maximum Mean Std. Deviation Enjoyment 16 67.00 98.00 78.2500 8.22598 Value 16 70.00 99.00 85.4375 8.29433 GPA 16 2.20 4.00 3.1625 .65307 Valid N (listwise) 16 Assumption Testing Assumption of Linearity The multiple regression requires that the assumption of linearity be met. Linearity was examined using a scatter plot. The assumption of linearity was met. See Figure 1 for the matrix scatter plot. Assumption of Bivariate Normal Distribution The multiple regression requires that the assumption of bivariate normal distribution be met. The assumption of bivariate normal distribution was examined using a scatter plot. The assumption of bivariate normal distribution was met.. See Figure 1 for the matrix scatter plot. Assumption of Multicollinearity A Variance Inflation Factor (VIF) test was conducted to assure the absence of multicollinearity. This test was run because if a predictor variable (x) is highly correlated with another predictor variable (x), they essentially provide the same information about the criterion variable. If the Variance Inflation Factor (VIF) is too high (greater than 10), then multicollinearity is present. Acceptable values are between 1 and 5. The absence of multicollinearity was met between the variables in this study. See Table 2 collinearity statistics. Table 2 Collinearity Statistics Coefficientsa Model Collinearity Statistics Tolerance VIF 1 Enjoyment .873 1.145 Value .873 1.145 a. Dependent Variable: GPA Results A multiple regression was conducted to see if there was a predictive relationship between the criterion variable (GPA) and the linear combination of predictor variables (enjoyment and value of learning) for high school students. The predictor variables were enjoyment and value of learning. The criterion variable was GPA. The researcher rejected the null hypothesis at the 95% confidence level where F(2, 13) = 7, p = .008. There was a statistical relationship between the predictor variables and the criterion variable. See Table 3 for regression model results. Table 3 Regression Model Results ANOVAa Model Sum of Squares df Mean Square F Sig. 1 Regression 3.379 2 1.690 7.277 .008b Residual 3.018 13 .232 Total 6.398 15 a. Dependent Variable: GPA b. Predictors: (Constant), Value, Enjoyment The model’s effect size was large where R = .727. Furthermore, R2 = .528 indicating that approximately 52.8% of the variance of criterion variable can be explained by the linear combination of predictor variables.