Correlation

A College Algebra instructor suspects there is a relationship between the number of previous courses a student has had using the graphing calculator and the final average of the student in the current Algebra course. The data is as follows:

Draw a Scatter Plot, compute the correlation coefficient ( r ), state Ho and Ha, test the Hypothesis using , and give the conclusion.

For this section and the one that follows we must turn "on" the diagnostic capabilities of the calculator.
Press Arrow down to DiagnosticOn Press

Next, begin by entering the data into the calculator.
Press

Press (the lower left screen appears) Always start from a clear list.

Now ENTER the X values into LIST1 and the Y values into LIST2. remember to press after each entry. ( you should be looking at top right screen)

To see a Scatter Plot of this data we will go to the STAT PLOT menu so press Y= . ( this screen will appear)

Press Make sure "ON" is highlighted and press

Next Arrow down to Scatter Plot and press Make sure Xlist : L1 , Ylist : L2 You may choose any Mark you desire. I will choose

You can now press to have the calculator automatically adjust the window to the data. You will need to extend zoom settings to finish this problem. Now as always we must adjust the WINDOW to fit the data. Press For our data Xmin= -1, Xmax= 3, Xscl= 1, Ymin= 75, Ymax= 100, Yscl= 5

Next press . (you will see this screen)

As you can see from the screen there appears to be a positive correlation. Now to determine the correlation coefficient we will go to the Statistical Calculations Menu . For this problem our Null and Alternative Hypothesis are as follows:

Ho: there is no linear relationship
Ha: there is a linear relationship

Press

Arrow right to "CALC" and then highlight 4 : LinReg (aX + b)
(the screen will automatically change to the screen below left)

Press . (see screen above right.)

Now by default the calculator will choose LIST1 and LIST2 so we can press . you will see this screen)

If you are not using LIST1, LIST2 then you must enter the X-LIST, Y-LIST in that order before you press ENTER!!.

As you see from the screen the Pearson Product Moment Coefficient is r = 0.725
If you do not see " r " on your screen you must turn on the Diagnostic.

For our problem the critical value from the tables* is c.v. = 0.632
[We are using a =0.05 and there are [10 Ð 2] = 8 degrees of freedom] Since our r = 0.725 > 0.632 we reject Ho. Therefore there is sufficient evidence at alpha = .05 level to reject the claim of no linear relationship.

Using the Linear Regression T-Test found on the calculator: First press Arrow left to TESTS then Arrow up to E : LinRegTTestÉ
Press
Make sure you enter the appropriate list and frequency. You will always choose . (see screen)

Arrow down to "Calculate" and press . (see screens below.)

As you can see from the screen our p-value is 0.176 which is less than 0.05, therefore we should reject Ho.

You will notice the calculator also gives the Correlation Coefficient (r), the T test statistic, and the coefficients to the equation for "the line of best fit"