Project:

I.  Data Set 1
 A.  On the graph paper draw a scatter diagram of the data, with the independent
     (explanatory) variable plotted on the X axis and the dependent (responsive) variable
     plotted on  the Y axis.

Price of a Gallon of Regular Gasoline
Source:  Energy Information Administration
Official Energy Statistics from the US Government

May, Year Dollars
1976 $0.592
1980 $1.217
1984 $1.147
1988 $0.91
1992 $1.179
1996 $1.299
2000 $1.617
2004 $2.041
2008 $4.199

 

Using the TI-83 to graph your data
1.  Enter the independent data (x) into L1 and the dependent data (y) into L2.
2.  Use the "2nd" and "Y =" keys to access the STATPLOT menu.
3.  Press "Enter" to enter STATPLOT. 

4.  Use the "Arrow" keys  and "Enter" to match the display on the right.
    a.  Turn "ON" STATPLOT
    b.  Choose the first "TYPE"
    c.  Choose L1 for the independent data location.
    d.  Choose L2 for the dependent data location.
    e.  Choose the first "MARK".

5.  Select "WINDOW".
6.  Enter the settings you see on the right.
     a.  The range of the independent variable (area) is 1976 to 2008. 
          Set the XMin and Xmax to straddle those values.  Starting at 1972, go to
          2012, in steps of 4.
     b.  The range of the dependent variable (price) is 0.592 to 4.199.  Set the 
          YMin and Ymax to straddle those values.  Starting at 0.5, go to 4.3, in 
         steps of 0.1.

7.  Select "GRAPH" to display your data.

Use the TI-83graph as a guide, you get:

     B.  Include the four step hypothesis test.  Using a 0.01 level of significance, test for the
          existence of a simple linear correlation between year and price of a gallon of regular gasoline.

     Step 1:
     Ho: Slope = 0.  There is no Linear correlation..
     H1:  Slope does not equal 0.  Claim, there appears to be a linear correlation.

     Step 2:  The level of significance is 0.01

     Step 3:

Using the TI-83 to calculate the p-value.
  1. Press the "STAT" button.
  2. Use the right arrow to highlight the "TESTS" selection.
  3. Use the down arrow to highlight "E: LinRegTTest".  Then press "ENTER".
  4. The Xlist should be L1.  If not, enter L1 by pressing "2nd", "1" and "ENTER".
  5. The Ylist should be L2.  If not, enter L2 by pressing "2nd", "2" and "ENTER".
  6. Frequency should be "1".
  7. Select the "not equal" ()
  8. Use the down arrow to highlight "Calculate and press "ENTER".
  9. Read the p value from the screen.  Remember to divide by 2.
  10. Press "CLEAR" to clear the screen. 

Label the level of significance and p-values on the following diagram.

     Using LinRegTTest, p value =

     Step 4:
     "Fail to Reject the Null Hypothesis.  Claim is not supported.  There does not appear to be a linear regression.

     C.  If statistical feasible,
          Since the claim was not supported, you cannot use the linear regression equation to answer the questions.
           i.  What is the regression equation?            

           ii.  Use the regression equation to fill in the table (point estimates) for the years.

May, Year Dollars
2002  
2010  
2030  

          iii.  For each year, do you feel your prediction is reliable or unreliable?  Explain your decision.
               

          iv.  Plot the above points, on your scatter diagram (Problem IA) and draw regression line through them.

II.  Date Set 2

A.  On the graph paper draw a scatter diagram of the data, with the independent
      (explanatory) variable plotted on the X axis and the dependent (responsive) variable
      plotted on  the Y axis.

Price of a Gallon of Regular Gasoline
Source:  Energy Information Administration
Official Energy Statistics from the US Government

May, Year Dollars
2001 $1.640
2002 $1.404
2003 $1.514
2004 $2.041
2005 $2.176
2006 $2.917
2007 $3.052
2008 $4.199

 

TI Graph

Using the TI graph as a model

     B.  Include the four step hypothesis test.  Using a 0.01 level of significance, test for the
           existence of a simple linear correlation between year and price of a gallon of regular gasoline.

     Step 1:
     Ho: Slope = 0.  There is no Linear correlation..
     H1:  Slope does not equal 0.  Claim, there appears to be a linear correlation.

     Step 2:  The level of significance is 0.01

     Step 3:

Using the TI-83 to calculate the p-value.
  1. Press the "STAT" button.
  2. Use the right arrow to highlight the "TESTS" selection.
  3. Use the down arrow to highlight "E: LinRegTTest".  Then press "ENTER".
  4. The Xlist should be L1.  If not, enter L1 by pressing "2nd", "1" and "ENTER".
  5. The Ylist should be L2.  If not, enter L2 by pressing "2nd", "2" and "ENTER".
  6. Frequency should be "1".
  7. Select the "not equal" ()
  8. Use the down arrow to highlight "Calculate and press "ENTER".
  9. Read the p value from the screen.  Remember to divide by 2.
  10. Press "CLEAR" to clear the screen. 


     Using LinRegTTest, p value =

     Step 4:
     "Reject the Null Hypothesis.
     Claim is supported.  The data appears to be linear.

     C.  If statistical feasible, 
               i.  What is the regression equation?

   Price of a gallon of regular gas = - $725.3849405 + $0.363059524

                ii.  Use the regression equation to fill in the table (point estimates) for the years.

May, Year Dollars
2002 $1.4601 $1.46
2010 $4.3647 $4.36
2030 $11.626 $11.63

          iii.  For each year, do you feel your prediction is reliable or unreliable?  Explain your decision.
                a.  2002:  Data is interpolated.  The prediction is reliable.
                b.  2010:  Even though the data is extrapolated, it is only a small amount beyond the data set.
                     The prediction should be reliable.
                c.  2030:  The data is extrapolated a large amount beyond the data set.  The prediction is unreliable.

          iv.  Plot the above points, on your scatter diagram (Problem IIA) and draw the regression line through them.

Part III. 
If both data sets were statistically significantly, then which data set and predicted values are more reliable and why?

Only the second data set was statistically significant.

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