In: Statistics and Probability
Table 1: Weight Suspended in kg | ||||
Luke | Rey | Anikin | ||
Week | 1 | 0 | 10 | 35 |
Week | 2 | 10 | 10 | 41 |
Week | 3 | 15 | 20 | 45 |
Week | 4 | 20 | 20 | 48 |
Week | 5 | 25 | 40 | 50 |
Week | 6 | 30 | 40 | 53 |
Week | 7 | 35 | 80 | 55 |
Week | 8 | 40 | 80 | 61 |
Week | 9 | 45 | 160 | 70 |
Week | 10 | 50 | 160 | 74 |
Week | 11 | 55 | 320 | 77 |
Week | 12 | 60 | 320 | 80 |
Table 2: Number of items Suspended | ||||||
Rocks | Kittens | Daggers | Wookies | |||
Luke | 25 | 15 | 30 | 3 | ||
Rey | 30 | 5 | 45 | 2 | ||
Anikin | 25 | 25 | 40 | 5 |
Q2. | Perform a simple linear regression on all three kid's progress. Hint: time is the x variable | ||||||||
and weight of stone suspended is the y variable. | |||||||||
Perform a simple linear regression on all three kid's progress. Show your work in the analysis tab, | |||||||||
putting the output in the designated spaces. | |||||||||
What is the regression equation for Luke? For Rey? For Anikin? Put your results in the indicated space. | |||||||||
What is the r2 for each kid? According to the p-value, which of the regression lines is statistically | |||||||||
significant at an alpha of 0.05? |
please make sure to do the p values. this is what I need to fill in:
Qyestion 2: | Luke | Rey | Anikin | ||||||
Regression equation | note: two significant digits is fine | ||||||||
r2 | note: two significant digits is fine | ||||||||
p-value | note: 4 significant digits is fine | ||||||||
Significant - Y/N? | |||||||||
|
|||||||||
Luke regression output here. | |||||||||
|
Given Data:
week |
Luke |
Rey |
Anikin |
1 |
0 |
10 |
35 |
2 |
10 |
10 |
41 |
3 |
15 |
20 |
45 |
4 |
20 |
20 |
48 |
5 |
25 |
40 |
50 |
6 |
30 |
40 |
53 |
7 |
35 |
80 |
55 |
8 |
40 |
80 |
61 |
9 |
45 |
160 |
70 |
10 |
50 |
160 |
74 |
11 |
55 |
320 |
77 |
12 |
60 |
320 |
80 |
The dependent variable for regression analysis here is the weight suspended by each kid i.e. y is the weight suspended and x is the week.
Regression output for Luke:
Coefficients |
Standard Error |
t Stat |
P-value |
||
Intercept |
-1.67 |
0.82 |
-2.04 |
0.068692 |
|
Week |
5.19 |
0.11 |
46.77 |
4.82E-13 |
|
ANOVA |
|||||
df |
SS |
MS |
F |
Significance F |
|
Regression |
1 |
3855.288 |
3855.288 |
2187 |
4.82E-13 |
Residual |
10 |
17.62821 |
1.762821 |
||
Total |
11 |
3872.917 |
|||
R Square |
0.995448 |
Adjusted R Square |
0.994993 |
Regression output for Rey:
Coefficients |
Standard Error |
t Stat |
P-value |
||
Intercept |
-77.73 |
32.39 |
-2.40 |
0.037315 |
|
week |
28.11 |
4.40 |
6.39 |
7.95E-05 |
|
ANOVA |
|||||
df |
SS |
MS |
F |
Significance F |
|
Regression |
1 |
113009.8 |
113009.8 |
40.81 |
7.95E-05 |
Residual |
10 |
27690.21 |
2769.021 |
||
Total |
11 |
140700 |
|||
R Square |
0.803197 |
Adjusted R Square |
0.783516 |
Regression output for Anikin:
Coefficients |
Standard Error |
t Stat |
P-value |
||
Intercept |
30.89 |
1.43 |
21.60 |
1.01E-09 |
|
week |
4.08 |
0.19 |
21.00 |
1.33E-09 |
|
ANOVA |
|||||
df |
SS |
MS |
F |
Significance F |
|
Regression |
1 |
2380.925 |
2380.925 |
440.98 |
1.33E-09 |
Residual |
10 |
53.99184 |
5.399184 |
||
Total |
11 |
2434.917 |
|||
R Square |
0.977826 |
Adjusted R Square |
0.975609 |
Luke |
Rey |
Anikin |
|
Regression equation |
|||
r2 |
0.99 |
0.80 |
0.98 |
p-value |
0.0000 |
0.0001 |
0.0000 |
Significant - Y/N? |
Y |
Y |
Y |
There is no question for Table-2