shawtybabi09
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Section 9.1 : 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. (References: example 1 - 4 pages 498 - 500; end of section exercises 15 - 22 pages 508 - 509)
The data below are the number of absences and the final grades of 9 randomly selected students from a statistics class.
Absences, x 4 7 10 8 13 6 19 12 9
Final grade, y 99 87 81 83 72 93 56 77 83
a: Scatter plot (3.5 points)
b: Type of correlation (positive linear correlation, negative linear correlation, or no linear correlation) (2.5 points)
c: Complete the table and find the correlation coefficient r.
(6 points)
x y xy x2 y2
4 99
7 87
10 81
8 83
13 72
6 93
19 56
12 77
9 83
Use the last row of the table to show the column totals.
n = 9
2. Construct a scatter plot including the regression line 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 below are the gestation periods, in months, of randomly selected animals and their corresponding life spans, in years.
Gestation, x 8 2.1 1.3 1 11.5 5.3 3.8 24.3
Life span, y 30 12 6 3 25 12 10 40
a: Scatter plot with regression line (3.5 points)
b: Type of correlation (positive linear correlation, negative linear correlation, or no linear correlation) (2.5 points)
c: Complete the table and find the correlation coefficient r.
(7 points)
x y xy x2 y2
8 30
2.1 12
1.3 6
1 3
11.5 25
5.3 12
3.8 10
24.3 40
Use the last row of the table to show the column totals.
n = 8
r =
3. Using the r calculated in problem 2c test the significance of the correlation coefficient using ? = 0.01 and the claim rho ? 0. Use the 7-steps hypothesis test shown at the end of this project. (References: example 7 page 505; end of section exercises 23 - 28 pages 510 - 511) (7 points) (Round the computed t to 3 decimal places.)
1. H0 :
Ha :
2. ? =
3.
4. the critical value(s) t0
5. Rejection region:
6. Decision:
7. Interpretation:
Section 9.2: Linear Regression
(References: example 1 - 3 pages 514 - 516; end of section exercises 13 -22 pages 518 - 520)
4. The data below are the gestation periods, in months, of randomly selected animals and their corresponding life spans, in years.
Gestation, x 8 2.1 1.3 1 11.5 5.3 3.8 24.3
Life span, y 30 12 6 3 25 12 10 40
a. Find the equation of the regression line for the given data. Round the line values to the nearest two decimal places. (4 points) Show your work.
b. Using the equation found in part a, predict the life span when the gestation is 10 months. Round to the nearest absence. (4 points)
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. (References: example 1 - 4 pages 498 - 500; end of section exercises 15 - 22 pages 508 - 509)
The data below are the number of absences and the final grades of 9 randomly selected students from a statistics class.
Absences, x 4 7 10 8 13 6 19 12 9
Final grade, y 99 87 81 83 72 93 56 77 83
a: Scatter plot (3.5 points)
b: Type of correlation (positive linear correlation, negative linear correlation, or no linear correlation) (2.5 points)
c: Complete the table and find the correlation coefficient r.
(6 points)
x y xy x2 y2
4 99
7 87
10 81
8 83
13 72
6 93
19 56
12 77
9 83
Use the last row of the table to show the column totals.
n = 9
2. Construct a scatter plot including the regression line 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 below are the gestation periods, in months, of randomly selected animals and their corresponding life spans, in years.
Gestation, x 8 2.1 1.3 1 11.5 5.3 3.8 24.3
Life span, y 30 12 6 3 25 12 10 40
a: Scatter plot with regression line (3.5 points)
b: Type of correlation (positive linear correlation, negative linear correlation, or no linear correlation) (2.5 points)
c: Complete the table and find the correlation coefficient r.
(7 points)
x y xy x2 y2
8 30
2.1 12
1.3 6
1 3
11.5 25
5.3 12
3.8 10
24.3 40
Use the last row of the table to show the column totals.
n = 8
r =
3. Using the r calculated in problem 2c test the significance of the correlation coefficient using ? = 0.01 and the claim rho ? 0. Use the 7-steps hypothesis test shown at the end of this project. (References: example 7 page 505; end of section exercises 23 - 28 pages 510 - 511) (7 points) (Round the computed t to 3 decimal places.)
1. H0 :
Ha :
2. ? =
3.
4. the critical value(s) t0
5. Rejection region:
6. Decision:
7. Interpretation:
Section 9.2: Linear Regression
(References: example 1 - 3 pages 514 - 516; end of section exercises 13 -22 pages 518 - 520)
4. The data below are the gestation periods, in months, of randomly selected animals and their corresponding life spans, in years.
Gestation, x 8 2.1 1.3 1 11.5 5.3 3.8 24.3
Life span, y 30 12 6 3 25 12 10 40
a. Find the equation of the regression line for the given data. Round the line values to the nearest two decimal places. (4 points) Show your work.
b. Using the equation found in part a, predict the life span when the gestation is 10 months. Round to the nearest absence. (4 points)
