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 ago
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