Question

Given a simple regression analysis, suppose that we have obtained the fitted regression model: yˆ = 6 + 8x and also the following statistics , ? = 3.20, ?̅ = 8, n = 42, and ii# Find the 95% confidence interval for the point where x =18. Interpret the result. å i=1 (x - x )2 =420 I

Answer #1

Fitting the simple linear regression model to the n= 27
observations on x = modulus of elasticity and y = flexural strength
given in Exercise 15 of Section 12.2 resulted in yˆ = 7.592, sYˆ =
.179 when x = 40 and yˆ = 9.741, sYˆ = .253 for x = 60.
a. Explain why sY ˆ is larger when x = 60 than when x = 40.
b. Calculate a confidence interval with a confidence level of 95%
for...

Consider the simple linear regression model and let e = y
−y_hat, i = 1,...,n be the least-squares residuals, where y_hat =
β_hat + β_hat * x the fitted values.
(a) Find the expected value of the residuals, E(ei).
(b) Find the variance of the fitted values, V ar(y_hat ). (Hint:
Remember that y_bar i and β1_hat are uncorrelated.)

Given the simple regression model Y= βo+ β1X and the regression
results that follow, test the null hypothesis that the slope
coefficient is 0 versus the alternative hypothesis of greater than
zero using probability of Type I error equal to 0.10 , and
determine the two-sided 95% and 99% confidence intervals.
a. A random sample of size = 36 with b1 = 7 and sb1 =1.7
b. A random sample of size n = 50 with b1= 7.3and sb1= 1.7...

In a simple linear regression analysis attempting to link
lottery sales (y) to jackpot amount (x), the following data are
available:
x
y
jackpot
($millions)
Sales
(millions)
12
60
14
70
6
40
8
50
The slope (b) of the estimated regression equation here is 3.5.
The intercept (a) is 20. Produce the 95% confidence interval
estimate of the population slope, β, and report the upper bound for
the interval.
a)5.02
b)4.66
c)7.23
d)3.72

In a small-scale regression study, we collected data on the
number of children in a family Xi and the number of
hours per week spent shopping Yi. The following data
were obtained:
i
1
2
3
4
5
6
Xi
2
6
3
1
1
9
Yi
13
17
12
12
9
22
Assume we performed a simple linear regression of Yi
on Xi, i.e. E(Yi) = ?0 +
?1Xi
(a) By hand compute X?X, X?Y, (X?X)-1, b,
Y^(means Y-hat),...

Consider the simple linear regression model y=10+30x+e where the
random error term is normally and independently distributed with
mean zero and standard deviation 1. Do NOT use
software. Generate a sample of eight observations, one each at the
levels x= 10, 12, 14, 16, 18, 20, 22, and 24.
Do NOT use software!
(a) Fit the linear regression model by least squares and find
the estimates of the slope and intercept.
(b) Find the estimate of ?^2 .
(c) Find...

Question 22
The following displays
the results of a bivariate regression analysis, which describes the
relationship between income (the IV or X variable) and violent
offending (the DV or Y variable). The table includes the regression
slope coefficient (b), standard error, sig. value and the 95%
confidence interval lower and upper bounds similar to how they
would appear from SPSS results.
Complete the
table by computing the t-statistic (or t-obtained) from the
information given in the table. The question is...

The following table is the output of simple linear regression
analysis. Note that in the lower right hand corner of the output we
give (in parentheses) the number of observations, n, used
to perform the regression analysis and the t statistic for
testing H0: β1 = 0 versus
Ha: β1 ≠ 0.
ANOVA
df
SS
MS
F
Significance F
Regression
1
61,091.6455
61,091.6455
.69
.4259
Residual
10
886,599.2711
88,659.9271
Total
11
947,690.9167
(n = 12;...

Using the simple random sample of weights of women from a data?
set, we obtain these sample? statistics: n=45 and x over bar equals
141.67 lb. Research from other sources suggests that the population
of weights of women has a standard deviation given by sigma equals
30.84 lbs.
a. Find the best point estimate of the mean weight of all women.
b. Find a 95?% confidence interval estimate of the mean weight of
all women.

Question 1:
In the normal error simple linear regression model, suppose all
assumptions hold except constancy of error variance with respect to
X. Suppose E(Y) = V(Y). What transformation of y works to stabilize
the variance?
Question 2:
Let Y1,Y2,...Yn be a random sample for a normal distribution with
mean 10 and variance 4. Let Y(k) denote the Kth order statistics of
this random sample. Approximate the probability:
P(Y(k) <= 8.5) , if K =15 and n = 50.
Please...

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