Question

Given are five observations for two variables, *x* and
*y*.

x_{i} |
1 | 2 | 3 | 4 | 5 |

y_{i} |
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 predict the value of
*y*when*x*= 3 (to 1 decimal).

ŷ =

Answer #1

X | Y | X * Y | X2 | Y2 | |

1 | 4 | 4 | 1 | 16 | |

2 | 6 | 12 | 4 | 36 | |

3 | 6 | 18 | 9 | 36 | |

4 | 11 | 44 | 16 | 121 | |

5 | 15 | 75 | 25 | 225 | |

Total | 15 | 42 | 153 | 55 | 434 |

Part a)

Scatter diagram indicate there is positive and strong relationship between variables.

Part b)

Equation of regression line is Ŷ = a + bX

b = 2.7

a =( Σ Y - ( b * Σ X) ) / n

a =( 42 - ( 2.7 * 15 ) ) / 5

a = 0.3

**Equation of regression line becomes Ŷ = 0.3 + 2.7
X**

Part c)

When X = 3

Ŷ = 0.3 + 2.7 X

Ŷ = 0.3 + ( 2.7 * 3 )

**Ŷ = 8.4**

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.

Given are five observations collected in a regression study on
two variables.
xi
2
6
9
13
20
yi
7
18
9
26
23
Which of the following scatter diagrams accurately represents
the data?
Scatter diagram #1
Scatter diagram #2
Scatter diagram #3
SelectScatter diagram #1Scatter diagram #2Scatter diagram #3Item
1
Compute b0 and b1 (to 1
decimal).
b1
b0
Complete the estimated regression equation (to 1 decimal).
= + x
Use the estimated regression equation to predict the value of
y...

Given are five observations collected in a regression study on
two variables.
xi
2
6
9
13
20
yi
7
18
9
26
23
Which of the following scatter diagrams accurately represents
the data?
Scatter diagram #1
Scatter diagram #2
Scatter diagram #3
SelectScatter diagram #1Scatter diagram #2Scatter diagram #3Item
1
Compute b0 and b1 (to 1
decimal).
b1
b0
Complete the estimated regression equation (to 1 decimal).
= + x
Use the estimated regression equation to predict the value of
y...

Given are five observations collected in a regression study on
two variables.
xi
2
6
9
13
20
yi
7
18
9
26
23
Which of the following scatter diagrams accurately represents
the data?
Scatter diagram #1
Scatter diagram #2
Scatter diagram #3
SelectScatter diagram #1Scatter diagram #2Scatter diagram #3Item
1
Compute b0 and b1 (to 1
decimal).
b1
b0
Complete the estimated regression equation (to 1 decimal).
= + x
Use the estimated regression equation to predict the value of
y...

Given are five observations collected in a regression study on
two variables.
xi
2
6
9
13
20
yi
7
18
9
26
23
Which of the following scatter diagrams accurately represents
the data?
Scatter diagram #1
atter diagram #1
Scatter diagram #2
Scatter diagram #3
SelectScatter diagram #1Scatter diagram #2Scatter diagram #3Item
1
Compute b0 and b1 (to 1
decimal).
b1
b0
Complete the estimated regression equation (to 1 decimal).
= + x
Use the estimated regression equation to predict the...

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=_____

Data for two variables, x and y, follow.
xi
1 2 3 4 5
yi
5 9 7 13 16
(a)
Develop the estimated regression equation for these data. (Round
your numerical values to two decimal places.)
ŷ = 2.20+2.60x
Compute the studentized deleted residuals for these data. (Round
your answers to two decimal places.)
xi
yi
Studentized
Deleted Residual
1
5
2
9
3
7
4
13
5
16

Given are five observations collected in a regression study on
two variables.
xi
2
6
9
13
20
yi
9
18
8
25
21
A. Develop the estimated regression equation for these data.
B.Use the estimated regression equation to predict the value of
y when
x = 13.

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
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...

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