Question

• 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(df_reg, df_res)=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

Answer 1

SOLUTION

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