Question

Consider the following data for two variables, *x* and
*y*.

x |
22 | 24 | 26 | 30 | 35 | 40 |
---|---|---|---|---|---|---|

y |
13 | 22 | 34 | 34 | 41 | 35 |

(a) Develop an estimated regression equation for the data of the
form *ŷ* = *b*_{0} +
*b*_{1}* x*. (Round

*ŷ* =

(b) Use the results from part (a) to test for a significant
relationship between *x* and *y*. Use *α* =
0.05

Find the value of the test statistic. (Round your answer to two decimal places.)

*F* =

Find the *p*-value. (Round your answer to three decimal
places.)

*p*-value =

Is the relationship between *x* and *y*
significant?

Yes, the relationship is significant.

No, the relationship is not significant.

(c)Develop a scatter diagram for the data.

Does the scatter diagram suggest an estimated regression equation
of the form *ŷ* = *b*_{0} +
*b*_{1}* x* +

Yes, the scatter diagram suggests that a linear relationship may be appropriate.

Yes, the scatter diagram suggests that a curvilinear relationship may be appropriate.

No, the scatter diagram suggests that a linear relationship may be appropriate.

No, the scatter diagram suggests that a curvilinear relationship may be appropriate.

(d) Develop an estimated regression equation for the data of the
form *ŷ* = *b*_{0} +
*b*_{1}* x* +

*ŷ* =

(e) Use the results from part (d) to test for a significant
relationship between * x*,

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the *p*-value. (Round your answer to three decimal
places.)

*p*-value =

Is the relationship between * x*,

Yes, the relationship is significant.

No, the relationship is not significant.

(f)Use the model from part (d) to predict the value of
*y* when * x* = 25. (Round your answer to
three decimal places.)

Answer #1

a

)Applying regression from excel: data -data analysis:

y^ =-3.7+1.138x

b)F =5.62

p value =0.077

No, the relationship is not significant.

Yes, the scatter diagram suggests that a curvilinear relationship may be appropriate.

d)

y^ =-165.5+12.07x-0.1766x^{2}

e)value of the test statistic =17.51

*p*-value =0.022

.

Yes, the relationship is significant.

f)

predicted value =-165.5+12.07*25-0.1766*25^2=25.875 (please try 25.887 if this comes wrong)

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0.84
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xi
1
2
3
4
5
yi
2
8
6
11
13
a) Develop the estimated regression equation by computing the
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b1 using
b1 =
Σ(xi −
x)(yi −
y)
Σ(xi −
x)2
and b0 = y −
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ŷ =?
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Average
Distance
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9
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11
1.12
16
0.82
21
0.63
27
0.50
30
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1
2
3
4
5
yi
4
6
6
11
15
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1.
2.
3.
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108
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178
40
5
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