Question
In: Statistics and Probability
A pediatric nurse is studying the number of hours infants sleep daily. He reviewed data from...
A pediatric nurse is studying the number of hours infants sleep daily. He reviewed data from eight randomly selected patients from the pediatric ward of the local hospital. The results were as follows, where x is the infant’s age in months, and y is the number of hours the infant slept daily: \
X 2 1 7 6 14 15 10 9
Y 14.50 15.00 14.25 13.5 12.75 12.00 13.25 13.75
(a) Construct the scatter plot that represents this data. [COMMENTS & HINTS: Include a descriptive title; label the axes.]
(b) Determine the centroid for this data set.
(c) Determine the line of best fit or trend line that models this data. [COMMENTS & HINTS: Construct the scatter plot in order to identify the trend line from it. Round off to the nearest thousandths is necessary.]
(d) Determine the correlation coefficient, r, which characterizes the association between these two variables.
(e) Describe verbally the association between the two variables.
(f) Compute the coefficient of determination, 2 r .
(g) What percentage of the variability between the two variables is not due to the relationship between them?
(h) Approximately how many hours would this linear regression model predict that a twelvemonth old baby would sleep daily?
Solutions
Expert Solution
(a)
(b)
| mean= | 8 | 13.625 |
| population sd= | 4.743 | 0.910 |
| median= | 8 | 13.625 |
(c) y = - 15.06-0.180x
following regression analysis information has been generated using ms-excel
| SUMMARY OUTPUT | ||||||||
| Regression Statistics | ||||||||
| Multiple R | 0.94114 | |||||||
| R Square | 0.885744 | |||||||
| Adjusted R Square | 0.866702 | |||||||
| Standard Error | 0.355186 | |||||||
| Observations | 8 | |||||||
| ANOVA | ||||||||
| df | SS | MS | F | Significance F | ||||
| Regression | 1 | 5.868056 | 5.868056 | 46.51376 | 0.000488 | |||
| Residual | 6 | 0.756944 | 0.126157 | |||||
| Total | 7 | 6.625 | ||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
| Intercept | 15.06944 | 0.246223 | 61.20249 | 1.28E-09 | 14.46696 | 15.67193 | 14.46696 | 15.67193 |
| X Variable 1 | -0.18056 | 0.026474 | -6.8201 | 0.000488 | -0.24534 | -0.11578 | -0.24534 | -0.11578 |
(d) correlation coefficeint=0.9411
(e) positive and strong association
(f) coefficient of determination=0.8857=88.57%
(g) percentage of the variability between the two variables is not due to the relationship between them?
100-88.57=11.43%
(h) for x=12, y= - 15.06-0.180*12=12.9
answer is 12.9 hours
orchestra answered 2 years agoRelated Solutions
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The following data give the number of hours 5 students spent
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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 gives the number of hours 7 students spent studying and their corresponding grades...
The following data gives the number of hours 7 students spent
studying and their corresponding grades on their exams.
Hours Spent Studying
0
1
2.5
3
4
4.5
5.5
gRADES
60
69
72
75
78
81
90
Step 1 of 3:
Calculate the correlation coefficient, r. Round your answer to
six decimal places.
Step 2 of 3:
Determine if r is statistically significant at the 0.050.05
level.
Step 3 of 3:
Calculate the coefficient of determination, r2r2. Round your
answer...
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 gives the number of hours 10 students spent studying and their corresponding grades...
The following data gives the number of hours 10 students spent
studying and their corresponding grades on their midterm exams.
Hours Spent Studying
0
0.5
1
2
2.5
3
4
4.5
5
5.5
Midterm Grades
60
63
75
81
84
87
90
93
96
99
Determine if r is statistically significant at the 0.01
level.
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.
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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
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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
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Step 2 of 5: Calculate the estimated variance of errors, se2.
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