Discuss tyhe below:
Correlation
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
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.
|
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
3. Using the r calculated in problem 1 test the significance of the correlation coefficient using a = 0.01 and the claim k = 0. Use the 7-steps hypothesis test shown at the end of this project.
1. H0 : k = 0
Ha : k ¹ 0
2. a =
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.