OVERVIEW of REGRESSION/CORRELATION

2.Fill in the following chart with the calculated values:

X(X - Mx)(X - Mx) 2Y (Y - My)(X - Mx)* (Y - My)

1065

2085

1270

2593

1575

950

2290

1478

1680

1099

TOTAL = > TOTAL =

NOW, DO THE FINAL SLOPE CALCULATION:b = / = _______?

NEXT DETERMINE THE y-INTERCEPT "a".(This is the value on the vertical Y-axis at which our "best fit" line crosses it because x = 0)."a" = My - b * Mx

You already have the My and Mx and now have the "b".Simply plug in those numbers to calculate "a".

a = __________ ?

OUR "BEST FIT" LINE EQUATION IS NOW COMPLETE:Y' =(b) X+(a) =______________________

WHERE Y' IS THE PREDICTED SCORE FOR A GIVEN X, "b" IS THE SLOPE OF THE LINE, AND "a" IS THE Y' INTERCEPT.(keep in mind that Y-prime values are estimates based on our line equation and NOT real data)

Another thought is are there any UNUSUAL values that might be throwing off the line equation?How could you handle such data?Would it make a big difference if deleted?

3a)Using the original equation, what would be YOUR predicted point total if you were to study 13 hours a week?____________What if you put in 29 hours a week? _____________

Be advised that predicting performance BEYOND the range of the x-values is called EXTRAPOLATION and is NOT a good idea as the estimated Y' value might be way off.

(b)Are either of these generated Y' values an extrapolation, and if so do you feel they are still realistic?

BUT, HOW "GOOD" IS OUR LINE EQUATION AT EXPLAINING THE RELATIONSHIP BETWEEN OUR INDEPENDENT VARIABLE (X) AND OUR DEPENDENT VARIABLE (Y)?HOW MUCH ERROR IS THERE?

4)

WE MUST CALCULATE THE CORRELATION COEFFICIENT (r)FOR OUR LINE EQUATION.

This "r" value not only allows us to determine the slope of the line, but also the strength or significance of the relationship between variable X and variable Y.The closer to + 1 or -1 the value of "r" is the stronger the correlation (relationship).If "r" = 0, there is no statistical relationship.

To calculate "r" we basically STANDARDIZE (as in calculating z-values) each X and Y variable.Remember the formula for "z"? For the X variables it isZx₁ =(X₁ - mean of X) / Sx and we do this for every Xvalue and for every Y value.The formula does not look that simple, however, but it works.

HERE IS THE FORMULA FOR CALCULATING "r"(remember that means SUM and that the (X²) = squaring each X value and then adding up (summing up) all those squared numbers ; whereas(X)² = adding up the X values and then squaring that sum.

r = [ n (X*Y) - (X) * (Y) ] / {[nX² - (X)² ] * [n Y² - (Y)²]}

USE THIS TABLE OFGIVEN AND CALCULATED VALUES TO INSERT INTO THIS EQUATION

XX2YY2X*Y

1

2

3

4

5

6

7

8

9

10

TOTALS >

The "n" equals the number of data pairs (x,y), which is 10 in this case.

SHOW your setup in the equation and then calculate the resulting r:r =_____________

Keep in mind that "r" MUST be between 0 and 1.If you get a value greater than 1, it's a math error.Always double-check your calculation anyway.NOW, calculate the COEFFICIENT OF DETERMINATION (r²)=_____%