Correlation/Linear Regression

1. Construct a scatter plot using excel for the given data. Determine whether there is a positive linear correlation, negative linear correlation, or no linear correlation. Complete the table and find the correlation coefficient r.

a. The data below are the ages and systolic blood pressure (measured in millimeters of mercury) of 9 randomly selected adults.

Age, x 38 41 45 48 51 53 57 61 65
Pressure, y 116 120 123 131 142 145 148 150 152

Part 1: Scatter plot

Part 2: Type of correlation (positive linear correlation, negative linear correlation, or no linear correlation)

Part 3: Complete the table and find the correlation coefficient r.

x y xy x2 y2
38 116
41 120
45 123
48 131
51 142
53 145
57 148
61 150
65 152

Use the last row of the table to show the column totals.
n = 9

r =

2. Construct a scatter plot using excel for the given data. Determine whether there is a positive linear correlation, negative linear correlation, or no linear correlation. Complete the table and find the correlation coefficient r. The data for x and y is shown below.

x 11 -6 8 -3 -2 1 5 -5 6 7
y -5 -3 4 1 -1 -2 0 2 3 -4

Part 1: Scatter plot

Part 2: Type of correlation (positive linear correlation, negative linear correlation, or no linear correlation)

Part 3: Complete the table and find the correlation coefficient r.
Answer
x y xy x2 y2
11 -5
-6 -3
8 4
-3 1
-2 -1
1 -2
5 0
-5 2
6 3
7 -4

Use the last row of the table to show the column totals.
n = 10

r =

3. Using the r calculated in problem 1 test the significance of the correlation coefficient using  = 0.01 and the claim  = 0. Use the 7-steps hypothesis test shown at the end of this project.
Answer:
1. H0 :  = 0
Ha :   0
2.  =
3. Find t
4. t0 =
5. Rejection region:
6. Decision:
7. Interpretation:

Linear Regression

4. The data below are the ages and systolic blood pressure (measured in millimeters of mercury) of 9 randomly selected adults.

Age, x 38 41 45 48 51 53 57 61 65
Pressure, y 116 120 123 131 142 145 148 150 152

a. Find the equation of the regression line for the given data. Round the line values to the nearest two decimal places.

b. Using the equation found in part a, predict the pressure when the age is 50. Round to the nearest year.

Instruction to copy a graph from Excel to a Word document
1. Create the graph in Excel.
2. Put your mouse in the graph area and left click. You will see little black boxes top, bottom, sides and the corners. (If desired, you can resize your graph by dragging these boxes with your mouse.)
3. With the boxes showing, choose EDIT COPY from the top menu.
4. Go to the Word document, place your mouse pointer when you want the graph and choose EDIT PASTE form the top menu.
5. Save your document.

Guidelines -- Hypothesis Testing Steps:
1. State H0 and Ha.
2. Specify the level of significance alpha .
3. Find the test statistic using the given data.
4. Find the critical value(s) t0. Use the method specified in the problem statement.
5. Define the rejection region using critical value(s)
6. Make a decision to reject or fail to reject the null hypothesis.
7. Interpret the decision in the context of the original claim.