Question
In: Statistics and Probability
The following data give the number of hours 55 students spent studying and their corresponding grades...
The following data give the number of hours 55 students spent studying and their corresponding grades on their midterm exams.
| Hours Studying | 2 | 5 | 5 | 5 | 5 |
|---|---|---|---|---|---|
| Midterm Grades | 68 | 74 | 81 | 92 | 99 |
Step 4 of 5 :
Construct the 90% confidence interval for the slope. Round your answers to three decimal places.
Solutions
Expert Solution
| X | Y | X2 | X * Y | Sxx =Σ (Xi - X̅ ) | Syy = Σ( Yi - Y̅ ) | Sxy = Σ (Xi - X̅ ) * (Yi - Y̅) | |
| 2 | 68 | 4 | 136 | 5.76 | 219.04 | 35.52 | |
| 5 | 74 | 25 | 370 | 0.36 | 77.44 | -5.28 | |
| 5 | 81 | 25 | 405 | 0.36 | 3.24 | -1.08 | |
| 5 | 92 | 25 | 460 | 0.36 | 84.64 | 5.52 | |
| 5 | 99 | 25 | 495 | 0.36 | 262.44 | 9.72 | |
| Total | 22 | 414 | 104 | 1866 | 7.2 | 646.8 | 44.4 |
X̅ = Σ (Xi / n ) = 22/5 = 4.4
Y̅ = Σ (Yi / n ) = 414/5 = 82.8
Equation of regression line is Ŷ = a + bX
b = ( n Σ(XY) - (ΣX* ΣY) ) / ( n Σ X2 - (ΣX)2
)
b = ( 5 * 1866 - 22 * 414 ) / ( 5 * 104 - ( 22 )2)
b = 6.1667
a =( ΣY - ( b * ΣX ) ) / n
a =( 414 - ( 6.1667 * 22 ) ) / 5
a = 55.6667
Equation of regression line becomes Ŷ = 55.6667 + 6.1667
X
Slope 
= b = 6.1667
Confidence Interval
90% confidence interval is -3.613 < <
15.946
orchestra answered 2 years agoRelated Solutions
The following data give the number of hours 55 students spent studying and their corresponding grades...
The following data give the number of hours 55 students spent
studying and their corresponding grades on their midterm exams.
Hours Studying
3
3
4
5
5
Midterm Grades
72
74
74
75
79
Step 1 of 5: Calculate the sum of squared errors (SSE). Use the
values b0=66.8000 and b1=2.0000 for the calculations. Round your
answer to three decimal places.
Step 2 of 5: Calculate the estimated variance of errors, se2.
Round your answer to three decimal places.
Step...
The following data give the number of hours 55 students spent studying and their corresponding grades...
The following data give the number of hours 55 students spent
studying and their corresponding grades on their midterm exams.
Hours Studying
00
22
22
33
55
Midterm Grades
7878
8787
8888
9393
9797
Table
Construct the 90% confidence interval for the slope. Round your
answers to three decimal places.
Construct the 90% confidence interval for the slope. Round your
answers to three decimal places.
Construct the 95% confidence interval for the slope. Round your
answers to three decimal places....
The following data give the number of hours 55 students spent studying and their corresponding grades...
The following data give the number of hours 55 students spent
studying and their corresponding grades on their midterm exams.
Hours Studying
2
5
5
5
5
Midterm Grades
68
74
81
92
99
Step 5 of 5 :
Construct the 99% confidence interval for the slope. Round your
answers to three decimal places.
The following data give the number of hours 5 students spent studying and their corresponding grades...
The following data give the number of hours 5 students spent
studying and their corresponding grades on their midterm exams.
Hours Studying
1
1
2
3
6
Midterm Grades
65
73
74
86
91
Step 1 of 5:
Calculate the sum of squared errors (SSE). Use the values
b0=65.9185 and b1=4.5698 for the calculations. Round your answer to
three decimal places.
Step 2 of 5:
Calculate the estimated variance of errors, s^2e. Round your
answer to three decimal places.
Step...
The following data give the number of hours 5 students spent studying and their corresponding grades...
The following data give the number of hours 5 students spent
studying and their corresponding grades on their midterm exams.
Hours Studying
1
1
2
3
6
Midterm Grades
65
73
74
86
91
Step 1 of 5:
Calculate the sum of squared errors (SSE). Use the values
b0=65.9185 and b1=4.5698 for the calculations. Round your answer to
three decimal places.
Step 2 of 5:
Calculate the estimated variance of errors, s^2e. Round your
answer to three decimal places.
Step...
The following data give the number of hours 5 students spent studying and their corresponding grades...
The following data
give the number of hours 5 students spent studying and their
corresponding grades on their midterm exams.
Hours Studying
1
1
3
5
6
Grades
74
86
87
96
98
Step 1 of 5 : Calculate the sum of squared
errors (SSE). Use the values b0=76.2307b0=76.2307 and
b1=3.7404b1=3.7404 for the calculations.
Step 2 of 5 : Calculate the estimated variance
of errors, s^2e. .
Step 3 of 5 : Calculate the estimated variance
of slope, s^2b1 ....
The following data give the number of hours 5 students spent studying and their corresponding grades...
The following data give the number of hours 5 students spent
studying and their corresponding grades on their midterm exams.
Hours Studying
0
1
3
4
6
Midterm Grades
73
78
85
90
93
Step 1 of 5:
Calculate the sum of squared errors (SSE). Use the values
b0=74.2456 and b1=3.4123 for the calculations. Round your answer to
three decimal places.
Step 2 of 5:
Calculate the estimated variance of errors, s2e . Round your
answer to three decimal places....
The following data give the number of hours 5 students spent studying and their corresponding grades...
The following data give the number of hours 5 students spent
studying and their corresponding grades on their exams.
Hours Studying
2
2
4
6
6
Grades
64
73
76
77
86
Step 5 of 5 :
Construct the 95% confidence interval for the slope. Round your
answers to three decimal places.
The following data give the number of hours 1010 students spent studying and their corresponding grades...
The following data give the number of hours 1010 students spent
studying and their corresponding grades on their midterm exams.
Hours Studying
0.50.5
0.50.5
11
22
22
3.53.5
3.53.5
4.54.5
55
5.55.5
Midterm Grades
6161
6565
6565
6565
7373
7878
7878
8383
9090
9090
Table
Copy Data
Step 1 of 5:
Calculate the sum of squared errors (SSE). Use the values
b0=59.1253b0=59.1253 and b1=5.5981b1=5.5981 for the calculations.
Round your answer to three decimal places.
Calculate the estimated variance of errors,...
The following data give the number of hours 5 students spent studying and their corresponding grades...
The following data give the number of hours 5 students spent
studying and their corresponding grades on their midterm exams.
Hours Studying
1
2
2
2
4
Midterm Grades
63
65
67
88
9
Step 1 of 5: Calculate the sum of squared errors (SSE). Use the
values b0=53.9167 and b1=9.5833 for the calculations. Round your
answer to three decimal places.
Step 2 of 5: Calculate the estimated variance of errors, . Round
your answer to three decimal places.
Step...
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