2. The summary output of the least squares fit for predicting wife's height from husband's height from a random sample of 170 married couples in Britain, where both partners are below 65 years is provided below. (Intercept) height.husband Estimate 43.5755 0.2863 Std. Error 4.6842 t value 9.30 Pr(>[t|) 0.0000 0.0000 0.0686 4.17 If Tom Cruise and his wife were from the UK, what would this model estimate his wife's height to be? (Tom Cruise is 69 inches) (i) (ii) Tom Cruise' first wife, Nicole Kidman, is 71 inches. Using the regression equation from the question above, calculate the residual between Nicole Kidman's actual height and Nicole Kidman's predicted height.

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2. The summary output of the least squares fit for predicting wife's height from
husband's height from a random sample of 170 married couples in Britain, where
both partners are below 65 years is provided below.
Estimate
43.5755
Std. Error
4.6842
Pr(>[t|)
0.0000
0.0000
t value
(Intercept)
height.husband
9.30
0.2863
0.0686
4.17
If Tom Cruise and his wife were from the UK, what would this
model estimate his wife's height to be? (Tom Cruise is 69 inches)
(i)
(ii)
Tom Cruise' first wife, Nicole Kidman, is 71 inches. Using the
regression equation from the question above, calculate the
residual between Nicole Kidman's actual height and Nicole
Kidman's predicted height.
3. Henry and Felix each draw independent random samples of size n = 100 from a
normal population with unknown mean u and known variance o? = 9. They both
construct 95% confidence intervals for u.
Will the width of Henry's confidence interval be the same as Felix's? Demonstrate
with the formula to construct confidence intervals, and comment.
Transcribed Image Text:2. The summary output of the least squares fit for predicting wife's height from husband's height from a random sample of 170 married couples in Britain, where both partners are below 65 years is provided below. Estimate 43.5755 Std. Error 4.6842 Pr(>[t|) 0.0000 0.0000 t value (Intercept) height.husband 9.30 0.2863 0.0686 4.17 If Tom Cruise and his wife were from the UK, what would this model estimate his wife's height to be? (Tom Cruise is 69 inches) (i) (ii) Tom Cruise' first wife, Nicole Kidman, is 71 inches. Using the regression equation from the question above, calculate the residual between Nicole Kidman's actual height and Nicole Kidman's predicted height. 3. Henry and Felix each draw independent random samples of size n = 100 from a normal population with unknown mean u and known variance o? = 9. They both construct 95% confidence intervals for u. Will the width of Henry's confidence interval be the same as Felix's? Demonstrate with the formula to construct confidence intervals, and comment.
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