162.0 172.1 186.8 176.4 184.9 186.8 Send data to calculator V 27,880.2 32,951.52 34,539.32 Figure 1 What is the slope of the least-squares regression line for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least two decimal places. (If necessary, consult a list of formulas.)

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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 x 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 son. The data are given in tabular form and also displayed in the Figure 1 scatter plot. Also given is the
product of the father's height and the son's height for each of the fifteen pairs. (These products, written in the column labelled "xy", may aid in calculations.)
Height of
father, x
(in
centimeters)
176.6
181.3
171.6
158.3
181.5
190.5
161.2
191.2
175.9
Height of son,
y
(in
centimeters)
173.4
188.9
180.7
175.0
176.3
189.2
168.5
194.8
179.5
191.3
171.2
200.0
170.1
192.2
162.0
186.8
184.9
Send data to calculator
190.9
172.1
176.4
186.8
xy
30,622.44
34,247.57
31,008.12
27,702.5
31,998.45
36,042.6
27,162.2
37,245.76
31,574.05
38,260
29,121.12
36,690.98
27,880.2
32,951.52
34,539.32
Height of son
(in centimeters)
Figure 1
210+
200+
190+
180-
170+
160-
150+
150
160
X
170 180 190 200
Height of father
(in centimeters)
210
What is the slope of the least-squares regression line for these data? Carry your intermediate computations to at least four decimal places and round your
answer to at least two decimal places. (If necessary, consult a list of formulas.)
Transcribed Image Text: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 x 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 son. The data are given in tabular form and also displayed in the Figure 1 scatter plot. Also given is the product of the father's height and the son's height for each of the fifteen pairs. (These products, written in the column labelled "xy", may aid in calculations.) Height of father, x (in centimeters) 176.6 181.3 171.6 158.3 181.5 190.5 161.2 191.2 175.9 Height of son, y (in centimeters) 173.4 188.9 180.7 175.0 176.3 189.2 168.5 194.8 179.5 191.3 171.2 200.0 170.1 192.2 162.0 186.8 184.9 Send data to calculator 190.9 172.1 176.4 186.8 xy 30,622.44 34,247.57 31,008.12 27,702.5 31,998.45 36,042.6 27,162.2 37,245.76 31,574.05 38,260 29,121.12 36,690.98 27,880.2 32,951.52 34,539.32 Height of son (in centimeters) Figure 1 210+ 200+ 190+ 180- 170+ 160- 150+ 150 160 X 170 180 190 200 Height of father (in centimeters) 210 What is the slope of the least-squares regression line for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least two decimal places. (If necessary, consult a list of formulas.)
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Step 1

It is given that the random variable x denoting the height ( in cms ) of human father and the variable y denoting the height at maturity ( in cms ) of the father’s oldest son.

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