For the following data:- X Y 3 2 5 6 4 9 2 3 5 6 5 4 Find the regression equation for predicting Y from X Use the regression equation to find a predicted Y for each X. Does the regression equation account for a significant portion of the variance in the Y scores? Use α = .05 to evaluate the F-ratio.
For the following data:- X Y 3 2 5 6 4 9 2 3 5 6 5 4 Find the regression equation for predicting Y from X Use the regression equation to find a predicted Y for each X. Does the regression equation account for a significant portion of the variance in the Y scores? Use α = .05 to evaluate the F-ratio.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 30PPS
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Concept explainers
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Question
- For the following data:-
|
X |
Y |
|
3 |
2 |
|
5 |
6 |
|
4 |
9 |
|
2 |
3 |
|
5 |
6 |
|
5 |
4 |
- Find the regression equation for predicting Y from X
- Use the regression equation to find a predicted Y for each X.
- Does the regression equation account for a significant portion of the variance in the Y scores? Use α = .05 to evaluate the F-ratio.
please use the table in the attached image
Transcribed Image Text:The F Distribution*
*Table entries in lightface type are critical values for the 05 level of significance.
Boldface type values are for the .01 level of significance.
Criticał
Degrees of
Freedom:
Denominator
Degrees of Freedom: Numerator
3.
4
7
8
9
10
11
12
14
16
20
1
239
200
4999 5403 5625
216
230
5764
161
225
234
237
241
242
243
244
246
6106 6142 6169 6208
245
248
4052
5859
5928
5981
6022
6056
6082
19.36
19.37
19.38
19.41 19.42 19.43 19.44
99.42 99.43 99.44 99.45
2
18.51 19.00 19.16 19.25 19.30 19.33
19.39
19.40
98.49 99.00 99.17 99.25 99.30 99.33
99.34
99.36 99.38
99.40 99.41
8.88
28.24 27.91 27.67
8.94
8.84
8.81
8.69 8.66
27.23 27.13 27.05 26.92 26.83 26.69
10.13 9.55 9.28
9.12
9.01
8.78
8.76
8.74
8.71
3.
34.12 30.92 29.46 28.71
27.49 27.34
6.04
5.96
14.54 14.45 14.37 14.24 14.15 14.02
6.94
6.59
6.39
6.26
6.16
6.09
6.00
5.91
5.87
7.71
21.20 18.00 16.69 15.98
4
5.93
5.84
5.80
15.52 15.21 14.98
14.80 14.66
6.61
5.79
5.19
5.05
4.95
4.88
4.82
4.78
4.74
4.70
1.68
1.61
1.60 1.56
9.68
5
5.41
16.26 13.27 12.06 11.39 10.97 10.67 10.45
10.27 10.15
10.05
9.96
9.89
9.77
9.55
4.15
8.10
5.14 4.76
4.53
4.10
4.06
4.39
8.75
4.00
7.72
6
5.99
4.28
4.21
4.03
3.96
3.92 3.87
13.74 10.92 9.78
9.15
8.47
8.26
7.98
7.87
7.79
7.60
7.52
7.39
3.79
3.73
6.84
4.74 4.35
3.97
3.87
3.68
3.63
3.60
5.59
12.25
3.49
6.27
7
4.12
3.57
3.52
3.44
9.55 8.45
7.85
7.46
7.19
7.00
6.71
6.62
6.54
6.47
6.35
6.15
3.50
6.19
3.28
5.67
4.46 4.07
3.69
3.58
6.37
3.39
5.91
3.34
3.31
3.23
5.56
5.32
3.84
3.44
3.20
5.48
3.15
5.36
8
11.26
8.65 7.59
7.01
6.63
6.03
5.82
5.74
5.12
3.37
3.23
3.29.
5.62
3.18
3.13
3.10
3.07
5.11
4.26 3.86
3.02
3.63
6.42
9.
3.48
2.98
2.93
10.56
8.02 6.99
6.06
5.80
5.47
5.35
5.26
5.18
5.00
4.92
4.80
3.07
5.06
2.97
3.02
4.95
2.91
4.71
2.94
4.96
10.04
3.48
3.33
5.64
3.22
3.14
5.21
2.86
4.60
4.10 3.71
2.82
4.52
10
2.77
7.56 6.55
5.99
5.39
4.85
4.78
4.41
3.09
5.07
2.95
2.90
4.84
9.65
3.59
6.22
3.20
5.32
2.82
4.46
I 1
3.98
3.36
3.01
2.86
2.79
2.74
2.70 2.65
7.20
5.67
4.88
4.74
4.63
4.54
4.40
4.29
4,21
4.10
3.26
5.41
3.00
4.82
2.80
4.39
2.76
4.30
3.49
2.69
3.11
5.06
2.92
2.85
4.50
2.72
4.22
2.64
2.60 2.54
4.75
9.33
3.88
6.93 5.95
12
4.65
4.16
4.05
3.98
3.86
2.67
4.10
2.63
3.02
4.86
2.92
2.84
2.77
2.72
2.60
4.67
9.07
3.80
6.70 5.74
2.55
3.85
3.18
2.51
3.78
13
3.41
2.46
5.20
4.62
4.44
4.30
4.19
4.02
3.96
3.67
2.85
2.65
4.03
14
4.60
3.74
3.34
3.11
2.96
2.77
2.70
2.60
2.56
2.53
2.48
2.44
2.39
8.86
6.51
5.56
5.03
4.69
4.46
4.28
4.14
3.94
3.86
3.80
3.70
3.62 3.51
2.79
2.59
2.55
2.70
4.14
2.64
2.48
2.43
2.39
3.56 3.48
2.90
2.51
2.33
4.54
8.68
15
3.68
3.29
3.06
6.36
5.42
4.89
4.56
4.32
4.00
3.89
3.80
3.73
3.67
3.36
2.66
2.59
3.89
2.54
2.8.5
4.44
2.74
2.49
2.45
2.42
2.37
2.28
3.37 3.25
16
4.49
3.63
3.24
3.01
2.33
8.53
6.23
5.29
4.77
4.20
4.03
3.78
3.69
3.61
3.55
3.45
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