Final answer:
The question pertains to the use of a linear regression equation, specifically îy = -173.51 + 4.83x, to calculate predicted y-values (or 'y hat') for a given x-value indicating a student's third exam score to predict their final exam score.
Step-by-step explanation:
The question relates to the concept of linear regression, which is a method used in statistics to model the relationship between a dependent variable and one or more independent variables. The equation îy = d is used to calculate the predicted value (îy, or "y hat") of the dependent variable for each data point. The equation îy = -173.51 + 4.83x represents the line of best fit, where 'x' is the independent variable (third exam score) and 'y' is the dependent variable (final exam score).
To calculate a predicted value using this equation, substitute the x-value (third exam score) into the equation and solve for îy. For example, using x = 90, the equation becomes îy = -173.51 + 4.83(90), which calculates to a predicted îy-value of 261.19. This indicates that, based on the regression model, a student who scores 90 on the third exam is predicted to score approximately 261.19 on the final exam.
However, it's important to consider the reliability of the predictions, especially when extrapolating beyond the range of observed x-values. The correlation coefficient (r = 0.6631) and the coefficient of determination (r² = .43969) give some measure of the strength and the proportion of variance explained by the line of best fit, respectively. When making predictions, caution should be taken as the actual scores may vary from the predicted scores.