MATH 131 Lab 9 complete solutions correct answers key

MATH 131 Lab 9 complete solutions correct answers key

The goal of this lab is to test the linear correlation between the two Quantitative Variables from Lab 1; to find the equation of the regression line for the variables; and to use the line for prediction.

Important Note:  The interpretation of computer output is part of this lab, but the output itself is not sufficient to complete this lab.  You may use the scatter plot from the computer but it must be titled and labeled appropriately.  All other parts of the lab must be submitted on separate paper and answers must be given in complete sentences.

(1 point each)

1.   Consider the relationship between the two quantitative variables from Lab 1. The data can be represented as ordered pairs (x, y) where x is the independent or explanatory variable and y is the dependent or response variable (See p. 484 and p. 496 #19 & 20).

      When you choose x and y, consider if changes in one variable explain or even cause changes in the second variable? Call the explanatory (predictor) variable x and the response variable y.

      If you don’t see such a relationship, choose the value of the Quantitative Variable  for x and the value of the Quantitative Variable  for y.

      Use Minitab to construct a scatter plot for your 40 ordered pairs of data. Clearly label your graph.  Include a label and scale for both axes and a title.

2.   Comment about the information shown in the scatter plot, in terms of any apparent linear correlation (See p.487).  Give a reasonable estimate for the linear correlation coefficient based on the graph.

3.   Find the value for r, the linear correlation coefficient, using Minitab.

4.   Perform a hypothesis test of the significance of r (Use), the linear correlation coefficient.  Clearly state the null and alternative hypothesis.  Follow Example 6 (See p. 491).

                        - State your conclusion clearly and completely.

                        - Does your answer agree with your response to #2 above?

5.   Regardless of the significance of the correlation coefficient from #3 above, find the equation               of the regression line, using Minitab.

                        -Should you use this line for prediction purposes?  Why or why not?  (See p. 504)

6.   What is the slope of your regression line?  Write a statement interpreting the meaning of the slope for your data.  [For example, if the slope is 4.5 and x is number of terms served by a U.S. senator and y is the age of the senator, you could say that for every increase of 1 term, you predict the average age of the US senator increases by 4.5 years.]

7.      What is the y - intercept of your line?  Write a statement interpreting the meaning of the

y-intercept for your data.  For your data set, does this y-intercept make sense?  Explain.

8.   Find 3 ordered pairs that could be on the regression line.  Specify the x values that you've chosen for the points (Make sure that you choose appropriate x values.) and show your calculations for .  Locate these 3 points on your scatter plot. Connect these 3 points and draw the regression line on the scatter plot from #1 above.

9.   Use one of the 3 points from #8 above to write a statement of prediction. Follow Example 3 (See p. 504).  [For example, if you chose x = 2 and computed =  58.4, write the statement as

      "I predict a senator who has served 2 terms will have an average age of 58.4 years old."]

10. Summarize your results of this lab for someone who is not familiar with statistical terminology but might be interested in your data.  In other words, what kind of a general relationship did you find, if any, between these 2 variables?                                                                                                          

                                                                              Minitab Directions

Use the computer to do as many of the calculations as you can.  Provide careful answers to the questions asked, and show the work where specified.

Open the worksheet where you saved your lab data or enter your 40 ordered pairs in 2 columns on the worksheet.

To draw a scatter plot for # 1,

Select Graph from the main bar.

Select Scatterplot from the subdirectory and choose Simple.

Click on OK.

In the Y variables box,

Click one of the variables in left-hand box to be your  y.  Select.

In the X variables box,

Click one of the variables in left-hand box to be your  x.  Select.

Click on OK.

To find  r, the linear correlation coefficient  for # 3,

Select Stat from the main menu.

Select Basic Statistics from the subdirectory and Select correlation.

List the columns that contain the data.

Click on OK.

To find the equation of the linear regression line for # 5,

Select Stat from the main menu.

Select Regression from the subdirectory and Select regression. Response is your y and Predictor is your x.

Click on Result and select Regression equation.

        Click on OK twice.

                .