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In: Statistics and Probability
Exercises 2 In a survey, a statistician analyzed the relationship between the Mothers-Heights (explanatory variable x)...
Exercises 2
In a survey, a statistician analyzed the relationship between the Mothers-Heights (explanatory variable x) and the Daughters-Heights (response y) by using the regression method. When he drew the regression line, he found that at = 0 the predicted response is = 29.9, and at = 1 the predicted response is = 30.43. Suppose that the standard deviations of Daughters-Heights is = 2.6 and Mothers-Heights is = 2.35.
Please answer the following questions underneath each question.
1. Find the intercept “a” and slope “b” of the regression line of Daughters-Heights on Mothers-Heights.
Answer: a=
b=
2. If the difference between the heights of two different mothers is 10 inches,
what is the predicted difference between the heights of their two daughters
Answer:
3. Compute the value of the correlation “r” between the two variables.
Answer:
Solutions
orchestra answered 2 years agoRelated Solutions
A medical statistician wanted to examine the relationship between the amount of sunshine (x) and incidence...
A medical statistician wanted to examine the relationship
between the amount of sunshine (x) and incidence of skin
cancer (y). As an experiment he found the number of skin
cancers detected per 100,000 of population and the average daily
sunshine in eight counties around the country. These data are shown
below.
Average Daily Sunshine
5
7
6
7
8
6
4
3
Skin Cancer per 100,000
7
11
9
12
15
10
7
5
Find the least squares regression line....
A sports statistician is interested in determining if there is a relationship between the number of...
A sports statistician is interested in determining if there is a
relationship between the number of home team and visiting team
losses and different sports. A random sample of 526 games is
selected and the results are given below. Calculate the chi-square
test statistic chi Subscript 0 Superscript 2 to test the claim that
the number of home team and visiting team losses is independent of
the sport. Use alphaequals0.01.
Football
Baseball
Soccer
Basketball
Home Losses
39
156
25
83...
3) A sports statistician is interested in determining if there is a relationship between the number...
3) A sports statistician is interested in determining if there
is a relationship between the number of home team and visiting team
losses and different sports. A random sample of 526 games is
selected and the results are given below. Find the critical value Λ
2 0 to test the claim that the number of home team and visiting
team losses is independent of the sport. Use ΅ = 0.01.
Football
Basketball
Soccer
Baseball
Home Team Loss
39
156
25...
Suppose we have the following data on a dependent variable (Y) and an explanatory variable (X):...
Suppose we have the following data on a dependent variable (Y)
and an explanatory variable (X):
X Y
0 140
1 140
4 0
0 180
3 80
2 120
4 0
1 200
2 120
3 40
Calculate the simple linear regression equation by hand. Show
all your work. Using your result, predict the value of Y when X =
3.5. (15 points)
Calculate the R2and the adjusted
R2measures (by hand) and provide an interpretation of
what they tell us. (12 points)
Test (by hand) to see whether this is...
a)By hand, draw a scatter diagram treating x as the explanatory variable and y as the response variable
x
4
5
6
8
9
y
6
8
11
14
16
a)By hand, draw a scatter diagram treating x as the explanatory
variable and y as the response variable
b)Find the equation of the line containing the points (44,66)
and (9,16).
c)Graph the line found in part (b) on the scatter diagram.
d)By hand, determine the least-squares regression line.
e)Graph the least-squares regression line on the scatter
diagram.
f)Compute the sum of the squared residuals for the line found...
Consider a binary response variable y and an explanatory variable x. The following table contains the...
Consider a binary response variable y and an
explanatory variable x. The following table contains the
parameter estimates of the linear probability model (LPM) and the
logit model, with the associated p-values shown in
parentheses.
Variable
LPM
Logit
Constant
−0.78
−5.90
(0.03
)
(0.03
)
x
0.04
0.28
(0.07
)
(0.02
)
a. Test for the significance of the intercept and
the slope coefficients at the 5% level in both models.
Coefficients
LPM
Logit
Intercept
Slope
b. What is the...
Consider a binary response variable y and an explanatory variable x. The following table contains the...
Consider a binary response variable y and an
explanatory variable x. The following table contains the
parameter estimates of the linear probability model (LPM) and the
logit model, with the associated p-values shown in
parentheses.
Variable
LPM
Logit
Constant
−0.70
−6.60
(0.03
)
(0.03
)
x
0.04
0.18
(0.04
)
(0.03
)
a. Test for the significance of the intercept and
the slope coefficients at the 5% level in both models.
coefficient
LPM
Logit
intercept
slope
b. What is the...
(a)What is the explanatory variable and the response variable? (b) Find the correlation between boat registrations...
(a)What is the explanatory variable and the response
variable?
(b) Find the correlation between boat registrations and manatee
deaths. (Round to the hundredths place.)
(c) What percent of the variation in manatees killed is
explained by the model?
(d) Find the least squares regression line for these data.
(Round all values to the hundredths place.)
(e) Predict how many manatees may die if 792 boats are
registered. (Round to the nearest whole number.)
Year
manatees killed
powerboat registration
1995
50...
17.3 Consider a binary response variable y and an explanatory variable x. The following table contains...
17.3
Consider a binary response variable y and an
explanatory variable x. The following table contains the
parameter estimates of the linear probability model (LPM) and the
logit model, with the associated p-values shown in
parentheses.
Variable
LPM
Logit
Constant
−0.69
−6.30
(0.04)
(0.06)
x
0.05
0.15
(0.07)
(0.06)
a.
Test for the significance of the intercept and the slope
coefficients at a 5% level in both models.
Coefficients
LPM
Logit...
As part of a recent? survey, self-reported? heights, x, and measured? heights, y, were obtained for...
As part of a recent? survey, self-reported? heights, x, and
measured? heights, y, were obtained for males aged 12?16. Use the
Wilcoxon? signed-ranks test to test the claim that the matched
pairs have differences that come from a population with median
equal to zero at a significance level of alpha equals 0.1. Find the
null and alternate hypothesis, test statistic, critival value and
state the conclusion.
x
y
67
68.6
61
63
68
61.1
67
61
64
67.7
64
68.3...
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