Question

Consider the following set of ordered pairs.

x 4 1 2 5

y 5 1 3 6

a) Calculate the slope and y-intercept for these data.

b) Calculate the total sum of squares (SST).

c) Partition the sum of squares into the SSR and SSE.

Answer #1

We can use here Excel for regression equation

Step 1) Enter data in Excel .

Step 2) Data >>Data analysis >>Regression >>Select y and x values separately >>Ok

We have regression equation is

y=0.15+1.2x

a) Slope =1.2 and y intercept =0.15

b) SST=14.75

c) SSR=14.4 and SSE=0.35

Consider the following set of ordered pairs.
x 6 0 3 4 4 1
y 4 1 4 5 6 7
Assuming that the regression equation is y with caret = 3.750 +
0.250x and that the SSE = 20.0000, test to determine if the slope
is not equal to zero using alpha = 0.10.
a.) state the hypotheses
b.) what is the test statistic?
c.) what is the p value?
d.) state the conclusion

Consider the following set of ordered pairs,
x y
2 6
7 11
1 4
4 9
3 7
Assuming that the regression equation is y=3.519 + 1.142x and
that the SSE= 1.5755, test to determine if the slope is not equal
to zero using a=0.05.
Test statistic=
identify the critical values=
and last state the conclusion

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....

Consider the following set of ordered pairs shown below.
Assuming that the regression equation is y+ 0.833+ 1.000x and the
SSE=2.8332, construct a 90% confidence interval for x=2.
X: 5 1 4 4 3 1
Y:6 2 6 4 3 2
Calculate the upper and lower limits of the confidence
interval.
UCL=?
LCL=?

Consider the following set of ordered pairs.
x 6 0 3 4 4 1
y 4 1 4 5 6 7
a.) state the hypotheses
b.) what is the test statistic?
c.) what is the p value?
d.) state the conclusion

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?

Consider the data.
xi
1
2
3
4
5
yi
3
7
4
10
12
The estimated regression equation for these data is
ŷ = 0.90 + 2.10x.
(a)
Compute SSE, SST, and SSR using equations
SSE = Σ(yi −
ŷi)2,
SST = Σ(yi −
y)2,
and
SSR = Σ(ŷi −
y)2.
SSE=SST=SSR=
(b)
Compute the coefficient of determination
r2.
r2
=
Comment on the goodness of fit. (For purposes of this exercise,
consider a proportion large if it is...

Consider the data.
xi
1
2
3
4
5
yi
4
7
6
10
13
The estimated regression equation for these data is
ŷ = 1.70 + 2.10x.
(a) Compute SSE, SST, and SSR using equations SSE =
Σ(yi −
ŷi)2, SST =
Σ(yi −
y)2, and SSR =
Σ(ŷi −
y)2.
SSE=
SST=
SSR=
(b) Compute the coefficient of determination
r2.
r2=
Comment on the goodness of fit. (For purposes of this exercise,
consider a proportion large if it...

Given are five observations for two variables, and . 1 2 3 4 5 4
6 8 12 14
The estimated regression equation for these data is .
^y=1+2.6x
a. Compute SSE, SST, and SSR using the following equations (to 1
decimal). SSE=Σ(yi-^yi)
SST=Σ(yi-^yi) SSR=Σ(yi-^yi)
b. Compute the coefficient of determination r^2 (to 3 decimals).
Does this least squares line provide a good fit?
c. Compute the sample correlation coefficient (to 4
decimals)

Consider the following set of ordered pairs shown below.
Assuming that the regression equation is y with caret=1.601+0.788x
and the SSE=5.15, construct a 90% confidence interval for
x=5.
x
55
00
44
33
44
11
y
66
22
66
44
33
22
Calculate the upper and lower limits of the confidence
interval.
UCL
=
LCL
=

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