International Journal of Open Educational Resources
pretability of results . Standardizing the two continuous variables created an interpretable zero-point . The remaining three variables OER use , Pell eligibility , and Male were binary and coded with an interpretable zero . Standardizing the two continuous independent variables made interpretation more consistent with the interpretation of binary variables , that is , the estimated change in the outcome variable if the independent variable ( either standardized-continuous or binary ) increases by a rational one unit . In addition , standardizing the continuous variable made the interaction effect more interpretable .
Results
Table 1 below show the results of regressing course grade ( i . e ., dependent variable ) on OER , standardized previous GPA , standardized course difficulty , gender , Pell-eligibility , and the interaction between OER and standardized course difficulty ( i . e ., independent variables and the interaction term ). The multiple R equals 0.446 with a coefficient of determination ( R 2 ) of 0.199 , which indicates 19.9 % of the overall variance in the outcome , course grade , can be explained by the list of independent variables included in this study . The overall model is significant [ F ( 6,15,626 ) = 646.163 , p < 0.0001 ]. The zero-order correlation of OER with course grade was 0.025 which was significant ( p < 0.05 ). However , in the presence of all the other predictors , OER was not a significant predictor of course grade ( B = 0.025 , β = 0.005 , p = 0.469 ). All other predictors in the model were significant . Previous GPA is the strongest predictor ( B = 0.605 , β = 0.410 , p < 0.001 ) and accounts for 16.6 percent of the variance in course grade [ semi-partial coefficient ( 0.408 ) squared = 0.166 ]. The unstandardized coefficient of 0.605 means that there was a projected 0.605-point increase ( in a 5-point grade scale ) in student course grades with every unit ( i . e ., 1 SD ) increase in student previous GPA , holding other predictors constant . Importantly , the covariate of standardized course difficulty was significant in the presence of the other variables ( B = -0.349 , β = -0.169 , p < 0.001 ); that is a predicted decrease of 0.349 point in student course grades with every unit ( i . e ., 1 SD ) increase in course difficulty while holding other predictors constant . This pattern is also consistent with the zero-order correlation between course difficulty and course grade ( r = -0.159 ). Reasonably , the coefficient was negative , meaning that course grades tended to be lower as course difficulty increased . Standardized course difficulty was based on the aggregated failure rate of each course which was based on student course grades . However , because the standardized course difficulty was aggregated across multiple sections for each course and the student course grade was based on individual performance , the zero-order correlation between them was not problematic with only one percent shared variance ( r = -0.138 , r 2 = 0.019 ). This strategy to estimate course difficulty is recommended as there do not appear to be issues with multicollinearity but does require a large sample of sections and courses .
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