Assignment:
1 : 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.
The data for x and y is shown below.
x -5 -3 4 1 -1 -2 0 2 3 -4
y 11 6 -6 -1 3 4 1 -4 -5 8
a: Scatter plot
b: Type of correlation (positive linear correlation, negative linear correlation, or no linear correlation)c: Complete the table and find the correlation coefficient r rounded to 4 decimals.
x y xy x^2 y^2
-5 11
-3 6
4 -6
1 -1
-1 3
-2 4
0 1
2 -4
3 -5
-4 8
Use the last row of the table to show the column totals.
n = 10
r=(nΣxy-Σx Σy)/nΣx2-Σx2 nΣy2-Σy2
2. Construct a scatter plot and include the regression line on the graph 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. (References: example 1 - 4 pages 498 - 500; end of section exercises 15 - 22 pages 508 - 509)
A manager wishes to determine the relationship between the number of miles (in hundreds of miles) the manager's sales representative's travel per month and the amount of sales (in thousands of dollars) per month.
Miles traveled, x 2 3 10 7 8 15 3 1 11
Sales, y 31 33 78 62 65 61 48 55 90
a: Scatter plot with regression line
b: Type of correlation (positive linear correlation, negative linear correlation, or no linear correlation).
c: Complete the table and find the correlation coefficient r rounded to 4 decimals.
x y xy x^2 y^2
2 31
3 33
10 78
7 62
8 65
15 61
3 48
1 55
11 90
Use the last row of the table to show the column totals.
n = 9
r=(nΣxy-Σxy)/nΣx2-Σx2 nΣy2-Σy2
3. Using the r calculated in problem 2c test the significance of the correlation coefficient using α = 0.01 and the claim rho = 0. Use the 7-steps hypothesis test shown at the end of this project.
1. H0 :
Ha :
2. α
3. t=r/√(1-r2/n-2)
4. the critical value(s) t0.
5. Rejection region:
6. Decision:
7. Interpretation:
2: Linear Regression
4. A manager wishes to determine the relationship between the number of miles (in hundreds of miles) the manager's sales representative's travel per month and the amount of sales (in thousands of dollars) per month.
Miles traveled, x 2 3 10 7 8 15 3 1 11
Sales, y 31 33 78 62 65 61 48 55 90
Use the table developed in #2.
a. Find the equation of the regression line for the given data.
b. Using the equation found in part a, predict the sales when the mileage is 400 (remember the mileage is given in hundreds so convert 400 to hundreds).