Question

The following observations are obtained from a random sample of 10 individuals: Individual x y 1 9.08 5.25 2 4.23 3.58 3 6.88 4.75 4 10.3 5.38 5 8.09 4.27 6 10.6 5.79 7 4.50 3.41 8 8.32 5.75 9 7.17 4.74 10 9.45 5.43 Run a t-linear regression test on this data. (HINT: make sure you copy the numbers correctly!) What are the appropriate null and alternative hypotheses? H0:r=0H1:r≠0 H0:ρ=0H1:ρ<0 H0:ρ=0H1:ρ≠0 H0:r=0H1:r>0 H0:r=0H1:r<0 H0:ρ=0H1:ρ>0 What is the correlation coefficient? Round to 4 decimals. Number What is the coefficient of determination? Round to 4 decimals. Number Calculate the value of the test statistic. Round your response to at least 2 decimal places. |t|= Number What is the corresponding P-value for the test statistic? Round your response to at least 6 decimal places. Number Make a decision (hint: when in doubt, use the α=.05 significance level) Since α P, we the null hypothesis Help write a summary of the results of this hypothesis test: enough evidence in this sample to conclude there is a between the variables X and Y at the α= significance level because P= Number . What is the equation of the Regression line? Round the values to 4 decimal places y^= Number ⋅x+ Number Choose the correct Unlabeled Scatter plot from the choices below Maple plot

Answer #1

Hypothesis:

H0:ρ=0H1:ρ≠0

T = (coff.x - beeta)/SEx = 5.8

p value < 0.05

reject H0

Annual high temperatures in a certain location have been tracked
for a sample of 8 years. Let X represent the year and Y the high
temperature (in C∘).
x
y
5
33.06
6
30.48
7
27.2
8
24.42
9
22.34
10
17.96
11
16.38
12
13.8
Calculate the correlation coefficient. (Round to three
decimal places.)
r=
Let's test the significance of the correlation
coefficient at α=0.01 significance level.
H0: There is not a significant relationship between the year and
high...

12.4 Study the following Minitab output from a regression analysis
to predict y from x.
a. What is the equation of the regression
model?
b. What is the meaning of the coefficient of
x?
c. What is the result of the test of the slope of
the regression model? Let α = .10.Why is the t ratio
negative?
d. Comment on r2 and the
standard error of the estimate.
e. Comment on the relationship of the F
value to the...

The authors of a paper presented a correlation analysis to
investigate the relationship between maximal lactate level
x and muscular endurance y. The accompanying data
was read from a plot in the paper.
x
410
740
770
790
850
1035
1210
1240
1290
1390
1475
1480
1505
2200
y
3.80
3.90
4.80
5.30
3.90
3.40
6.40
6.88
7.55
4.95
7.90
4.45
6.50
8.90
Sxx = 2,619,073.214, Syy
= 39.4021, Sxy = 7632.018. A scatter plot shows
a linear pattern.
(a)...

Consider the following set of ordered pairs.
x 6 1 4 3 4 0
y 5 2 5 3 4 5
Assuming that the regression equation is y=3.375 + 0.208x and
that the SSE=6.9583, test to determine if the slope is not equal
to zero using α=0.10.
State the hypotheses. Choose the correct answer below.
A. H0: β ≠0 H1: β=0
B. H0: β=0 H1: β>0
C. H0: β=0 H1: β≠0
D. H0: β=0 H1: β<0
Calculate the test statistic....

The authors of a paper presented a correlation analysis to
investigate the relationship between maximal lactate level
x and muscular endurance y. The accompanying data
was read from a plot in the paper.
x
400
760
770
810
850
1035
1210
1260
1290
1410
1475
1480
1505
2200
y
3.80
4.10
4.80
5.30
3.90
3.40
6.40
6.88
7.55
4.95
7.70
4.45
6.70
8.90
Sxx = 2,614,773.214, Syy
= 38.2727, Sxy = 7544.396. A scatter plot shows
a linear pattern.
(a)...

Given are five observations collected in a regression study on
two variables.
x i
2
6
9
13
20
y i
7
18
9
26
23
1. Compute SSE, SST, and SSR (round to one decimals).
2. Compute the coefficient of determination (round to four
decimals).
3. Compute the mean square error (round to two decimals).
4. Compute the estimated standard deviation of
b1 (round to four decimals).
5. Compute the p-value and t value (test statistic) of
the t...

Study the following Minitab output from a regression analysis to
predict y from x. a. What is the equation of the regression model?
b. What is the meaning of the coefficient of x? c. What is the
result of the test of the slope of the regression model? Let α =
.10.Why is the t ratio negative? d. Comment on r2 and the standard
error of the estimate. e. Comment on the relationship of the F
value to the t...

A sociologist is interested in the relation between x = number
of job changes and y = annual salary (in thousands of dollars) for
people living in the Nashville area. A random sample of 10 people
employed in Nashville provided the following information.
x (number of job changes) 4 7 5 6 1 5 9 10 10 3
y (Salary in $1000) 34 33 32 32 32 38 43 37 40 33
In this setting we have Σx = 60,...

Consider the following set of ordered pairs.
x
5
1
2
4
4
y
6
1
0
6
5
Calculate the coefficient of determination and test its
significance using α=0.05.
A. Calculate the coefficient of determination.
R^2equals=
B. Determine the null and alternative hypotheses.
Determine the critical F-score, Fα.
Fα=
(Round to three decimal places as needed.)
Calculate the F-score for this test.
F=
(Round to three decimal places as needed.)
Reject or Do not reject?

Given are five observations for two variables, x and y .
xi
1
2
3
4
5
yi
53
58
47
21
11
Use the estimated regression equation is y-hat = 78.01 -
3.08x
A.) Compute the mean square error using
equation.
s^2 = MSE = SSE / n -2
[ ] (to 2 decimals)
B.) Compute the standard error of the estimate
using equation
s = sqrtMSE = sqrt SSE / n - 2
[ ] (to 2 decimals)...

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