Question

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)

**C.)** Compute the estimated standard deviation of
b1 using equation.

sb1 = s / sqrt ( xi - x-bar )^2

[ ] (to 4 decimals)

**D.)** Use the t -test to test the following
hypotheses (a=.05 ):

H0 = B1 = 0

Ha = B1 ≠ 0

Compute the value of the -test statistic (Enter negative values as negative numbers). [ ] (to 4 decimals)

THE P-VALUE IS: [ Less than .01, * between .01 and .02, * .02 and .05, * .05 and .10, * .10 and .20, * .20 and .40, * Greater than .40. ]

What is your conclusion? [ DO NOT REJECT ; REJECT ] Ho

**E.)**

Use the F -test to test the hypotheses in part
(**d**) at a .05 level of significance. Present the
results in the analysis of variance table format.

Complete the F table below. Calculate the Sum of Squares (to 1 decimal), the Mean Squares (to 1 decimal), and the F ratio (to 2 decimals).

Sourceof Variation |
Degreesof Freedom |
Sum of Squares(to 1 decimals) |
Mean Square(to 1 decimals) |
(to 2 decimals) |
-value(to 4 decimals) |

Regression | |||||

Error | |||||

Total |

What is the P -value? [ between .01 and .025 ; *between .025 and .05 ; * between .05 and .10 ; * greater than .10 ; * Lower than .01 ]

What is your conclusion, based on this F test?

We [ DO NOT REJECT ; REJECT ] Ho

Answer #1

E)

ANOVA | |||||

Sourse |
df |
SS |
MS |
F |
P-value |

Regression | 1 | 1464.1 | 1464.10 | 16.90 | 0.0261 |

Residual | 3 | 259.9 | 86.63 | ||

Total | 4 | 1724 |

The p-value is between .025 and .05.

The P-value from the t-test in D) should be equal to the P-value in E). The correct regression equation is y^ = 74.3 - 12.1 xi.

From D), we retain the Ho and conclude that the variable X does not have a significant effect on Y at 0.05 level of significance. Whereas from E), we reject Ho and conclude that the variable X has a significant effect on Y at 0.05 level of significance.

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)...

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...

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.

xi
2
6
9
13
20
yi
7
18
9
26
23
The estimated regression equation is ŷ = 7.6 +
.9x.
What is the value of the standard error of the estimate (to 4
decimals)?
What is the value of the t test statistic (to 2
decimals)?
What is the p-value?
- Select your answer -less than .01between .01 and .02between .02
and .05between .05 and .10between .10 and .20between .20 and
.40greater than .40Item 3
What is your...

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, 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)

Given are five observations for two variables, x and y.
X: 1 2 3 4 5
Y: 4 5 5 11 13
a. Try to approximate the relationship between x and y by
drawing a straight line through the data.
b. Develop the estimated regression equation by computing the
values of b0 and b1 (to 1 decimals).
y= _____ + ______x
c. Use the estimated regression equation to predict the value of
y when x=4 (to 1 decimals).
y=_____

Given are five observations for two variables, x and
y.
xi
1
2
3
4
5
yi
4
6
6
11
15
Which of the following scatter diagrams accurately represents
the data?
1.
2.
3.
What does the scatter diagram indicate about the relationship
between the two variables?
Develop the estimated regression equation by computing the the
slope and the y intercept of the estimated regression line
(to 1 decimal).
ŷ = + x
Use the estimated regression equation to...

Consider the data.
xi
1
2
3
4
5
yi
2
8
6
11
13
(a)
Compute the mean square error using
equation s2 = MSE =
SSE
n −
2
. (Round your answer to two decimal places.)
(b)
Compute the standard error of the estimate using equation
s =
MSE
=
SSE
n −
2
. (Round your answer to three decimal places.)
(c)
Compute the estimated standard deviation of
b1
using equation
sb1 =
s
Σ(xi −
x)2...

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