The output below is the result of investigating the predictive relationship betw

Question

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. Write out the line of best fit equation for this relationship. 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?

Explanation / Answer

Coefficient of Correlation = Sq.root(R Square) = Sq.root(0.771) = 0.878 as mentioned in the above table too.

The "F value'' and its p value test the overall significance of the regression model.  Specifically, they test the null hypothesis that all of the regression coefficients are equal to zero.  This tests the full model against a model with no variables and with the estimate of the dependent variable being the mean of the values of the dependent variable.  The F value is the ratio of the mean regression sum of squares divided by the mean error sum of squares.  Its value will range from zero to an arbitrarily large number

The p value is the probability that the null hypothesis for the full model is true (i.e., that all of the regression coefficients are zero).  For example, if p has a value of 0.01000 then there is 1 chance in 100 that all of the regression parameters are zero.

So in this case F >> 1 and its p value is almost 0 so we can say that freshman year score significantly tells us about the senior year science scores.

Output using the above mentioned linear regression equation goes like this

Y = -2.613 + (1.073*70) = 72.497

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