1. Greater than or less than? 2. Increase or decrease?

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1. Greater than or less than? 2. Increase or decrease?
9:19
AA
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O REGRESSION AND CORRELATION
Predictions from the least-
Shasia v
OC OD D
Sir Francis Galton, in the late 1800s, was the first to introduce the
statistical concepts of regression and correlation. He studied the
relationships between pairs of variables such as the size of parents and
the size of their offspring.
Data similar to that which he studied are given below, with the variable
denoting the height (in centimeters) of a human father and the variable
y denoting the height at maturity (in centimeters) of the father's oldest
(adult) son. The data are given in tabular form and also displayed in the
Figure 1 scatter plot, which gives the least-squares regression line as
well. The equation for this line is -92.69 + 0.49x.
Height of father, Height of son, y
(in centimeters)
(in centimeters)
159.5
172.6
187.2
176.8
186.6
186.9
200
174.9
178.4
176.1
175.1
19
158.3
176.0
161.2
167.8
191.8
188.9
17
201.7
188.9
181.6
189.6
15
183.4
179.2
193.8
190.7
210
172.0
182.1
191.0
195.4
Figure 1
173.2
171.5
Send data to Excel
Answer the following:
. Fill in the blank: For these data, heights of fathers that are greater
than the mean of the heights of fathers tend to be paired with heights
of sons that are
Choose one
the mean of the heights of sons.
2. Fil in the blank: According to the regression equation, for an
increa
se of one centimeter in father's height, there is a corresponding
Choose one
of 0.49 centimeters in son's height.
3. From the regression equation, what is the predicted son's height (in
centimeters) when the height of the father is 193.8 centimeters?
(Round your answer to at least one decimal place.)
4. What was the observed son's height (in centimeters) when the
height of the father was 193.8 centimeters?
Transcribed Image Text:9:19 AA www-awn.aleks.com O REGRESSION AND CORRELATION Predictions from the least- Shasia v OC OD D Sir Francis Galton, in the late 1800s, was the first to introduce the statistical concepts of regression and correlation. He studied the relationships between pairs of variables such as the size of parents and the size of their offspring. Data similar to that which he studied are given below, with the variable denoting the height (in centimeters) of a human father and the variable y denoting the height at maturity (in centimeters) of the father's oldest (adult) son. The data are given in tabular form and also displayed in the Figure 1 scatter plot, which gives the least-squares regression line as well. The equation for this line is -92.69 + 0.49x. Height of father, Height of son, y (in centimeters) (in centimeters) 159.5 172.6 187.2 176.8 186.6 186.9 200 174.9 178.4 176.1 175.1 19 158.3 176.0 161.2 167.8 191.8 188.9 17 201.7 188.9 181.6 189.6 15 183.4 179.2 193.8 190.7 210 172.0 182.1 191.0 195.4 Figure 1 173.2 171.5 Send data to Excel Answer the following: . Fill in the blank: For these data, heights of fathers that are greater than the mean of the heights of fathers tend to be paired with heights of sons that are Choose one the mean of the heights of sons. 2. Fil in the blank: According to the regression equation, for an increa se of one centimeter in father's height, there is a corresponding Choose one of 0.49 centimeters in son's height. 3. From the regression equation, what is the predicted son's height (in centimeters) when the height of the father is 193.8 centimeters? (Round your answer to at least one decimal place.) 4. What was the observed son's height (in centimeters) when the height of the father was 193.8 centimeters?
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