Question

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)

Answer #1

]

from above:

a)

SSE =1.200

SST =68.800

SSR =67.600

b)

coefficient of determination =0.983 ; this is a good fit

c)

correlation coefficient r= |
S_{xy}/(√S_{xx}*S_{yy})
= |
0.9912 |

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...

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
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 at least 0.55.)...

Consider the data.
xi
1
2
3
4
5
yi
3
7
5
11
14
The estimated regression equation for these data is
ŷ = 0.20 + 2.60x.
(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...

Consider the data.
xi
3
12
6
20
14
yi
65
35
50
15
20
The estimated regression equation for these data is
ŷ = 70 − 3x.
(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.
(Round your answer to three decimal places.)
r2
=
Comment on the goodness of fit....

Given are five observations for two variables, x and
y.
xi
1
2
3
4
5
yi
4
7
6
11
14
The estimated regression equation is = 1.2 + 2.4
x.
Compute the mean square error using the following equation (to
3 decimals).
Compute the standard error of the estimate using the following
equation (to 3 decimals).
Compute the estimated standard deviation b
1 using the following equation (to 3 decimals).
Use the t test to test the following hypotheses...

The data is given as follow.
Excel File: data14-17.xlsx
Xi 2
6
9
13 20
Yi 7
18
9
26 23
The estimated regression equation for these data is y=
7.6+.9x.
Compute SSE, SST, and SSR (to 1 decimal).
SSE
SST
SSR
What percentage of the total sum of squares can be accounted for
by the estimated regression equation (to 1 decimal)?
---------%
What is the value of the sample correlation coefficient (to 3
decimals)?
----------

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...

Given are five observations for two variables, x and y. xi 1 2 3
4 5 yi 4 7 6 12 15 The estimated regression equation is ? = 0.7 +
2.7x. Compute the mean square error using the following equation
(to 3 decimals). Compute the standard error of the estimate using
the following equation (to 3 decimals). Compute the estimated
standard deviation b1 using the following equation (to 3 decimals).
Use the t test to test the following hypotheses...

Given are five observations for two variables, x and
y.
xi
1
2
3
4
5
yi
2
8
6
11
13
a) Develop the estimated regression equation by computing the
values of b0 and
b1 using
b1 =
Σ(xi −
x)(yi −
y)
Σ(xi −
x)2
and b0 = y −
b1x.
ŷ =?
b) Use the estimated regression equation to predict the value of
y when
x = 2.

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