The output below is the result of investigating the predictive relationship between freshman year science scores and senior year science scores. Researchers wanted to see if they can predict senior year science scores from each student’s freshman year scores. Answer the following questions using the output below:
· What is the correlation coefficient (r) for the relationship between senior and freshman year scores?
· Does freshman year science scores significantly predict senior year science scores?
· Write out the F statistical string associated with this relationship. [F( dfreg, dfres)= F value, p=________]
· Write out the line of best fit equation for this relationship (Y=bX+a, substituting the b & a with values from the table).
· If someone scored a 70 on their freshman year science test, based on the line of best fit, what would their predicted senior year score be?
| Model Summary | ||||
| Model | R | R Square | Adjusted R Square | Std. Error of the Estimate |
| 1 | .878a | .771 | .770 | 5.80149 |
| a. Predictors: (Constant), freshman yr science score |
| ANOVAa | ||||||
| Model | Sum of Squares | df | Mean Square | F | Sig. | |
| 1 | Regression | 22478.445 | 1 | 22478.445 | 667.862 | .000b |
| Residual | 6664.150 | 198 | 33.657 | |||
| Total | 29142.595 | 199 | ||||
| a. Dependent Variable: senior yr science score | ||||||
| b. Predictors: (Constant), freshman yr science score |
| Coefficientsa | ||||||
| Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | ||
| B | Std. Error | Beta | ||||
| 1 | (Constant) | -2.613 | 2.192 | -1.192 | .235 | |
| freshman yr science score | 1.073 | .042 | .878 | 25.843 | .000 | |
| a. Dependent Variable: senior yr science score |