A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects 5 children and measures their height and head circumference. The data are summarized below.
Height_(inches)_-_x Head
Circumference_(inches)_-_y
26 17.3
24.5 17.1
27.75 17.6
26.5 17.3
27 17.5
(a) Treating height as the explanatory variable, x, use technology to determine the estimates of β0 and β1.
β0≈=b0=13.2857
(Round to four decimal places as needed.)
β1≈b1=0.1546
(Round to four decimal places as needed.)
Se=0.0570
(Round to four decimal places as needed.)
(c) A normal probability plot suggests that the residuals are normally distributed. Use technology to determine sb1.
sb1=__?__
(Round to four decimal places as needed.)
The statistical software output for this problem is:
Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 13.285714 + 0.15462185 x
Sample size: 5
R (correlation coefficient) = 0.96740327
R-sq = 0.93586908
Estimate of error standard deviation: 0.057002629
Parameter estimates:
Parameter | Estimate | Std. Err. | Alternative | DF | T-Stat | P-value |
---|---|---|---|---|---|---|
Intercept | 13.285714 | 0.61629533 | ≠ 0 | 3 | 21.557383 | 0.0002 |
Slope | 0.15462185 | 0.0233688 | ≠ 0 | 3 | 6.6165936 | 0.007 |
Hence,
c) sb1 = Standard error for Slope = 0.0234
A pediatrician wants to determine the relation that may exist between a child's height and head...
A pediatrician wants to determine the relation that exists between a child's height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences and obtains the accompanying data. (a) Find the least-squares regression line treating height as the explanatory variable and head circumference as the response variable. The least-squares regression line is (Round to four decimal places as needed.) Height, x (inches) Head circumference, y (inches) 27.75 17.7 24.5 17.1 25.5...
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I need help at the bottom of the page with - A normal probability plot suggests that the residuals are normally distributed - thank you! A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects 5 children and measures their height and head circumference. The data are summarized below. Height_(inches)_-_x Head Circumference_(inches)_-_y 27.5 17.5 27.75 17.6 25.5 17.1 25 16.9 26.5 17.3 (a) Treating height as the explanatory variable, x,...
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Question 24
A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects 5 children and measures their height and head circumference. The data are summarized below. A normal probability plot suggests that the residuals are normally distributed. Complete parts (a) and (b) below. Height (inches), x 27.75 27.5 26.75 25 25.55 Head Circumference (Inches), y 17.6 17.5 17.3 16.9 17.1 (a) Use technology to determine sp.. (Round to four decimal...
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a pediatrician wants to determine the relation that exists between a child's height,x, and head circumference, y,. She randomly selects 11 children from her practice, measures their heights and head circumferences, and obtains the least square regression equation of y= 0.0142x+13.589. interpret the y- intercept, if appropriate. a) for a head circumference of 0 inches, the height is predicted to be 13.589 inches b) for every inch increases in head circumference, the height increases by 0.142 inches, on average c)...
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