Consider a possible linear relationship between two variables that you would lik
ID: 3315038 • Letter: C
Question
Consider a possible linear relationship between two variables that you would like to explore.
Define the relationship of interest and a data collection technique.
Determine the appropriate sample size and collect the data.
Perform the appropriate analysis to determine if there is a statistically significant linear relationship between the two variables. Describe the relationship in terms of strength and direction.
Construct a model of the relationship and evaluate the validity of that model.
height (inches) weight (lbs) 1 64 134 2 68 120 3 67 115 4 71 128 5 70 134 6 71 118 7 66 106 8 66 126 9 64 114 10 68 130 11 68 123 12 69 122 13 69 125 14 68 111 15 68 125 16 66 119 17 70 132 18 72 132 19 67 117 20 64 101 21 69 128 22 68 134 23 67 127 24 68 127 25 65 139 26 64 113 27 68 147 28 66 132 29 69 132 30 65 105 31 66 127 32 69 130 33 67 128 34 65 122 35 69 157 36 66 121 37 69 147 38 67 117 39 69 132 40 68 118 41 71 123 42 66 130 43 66 122 44 68 107 45 68 118 46 66 125 47 71 148 48 66 150 49 69 127 50 68 128 51 65 118 52 66 125 53 71 149 54 67 107 55 68 133 56 68 124 57 67 112 58 67 127 59 69 134 60 67 138 61 69 126 62 70 129 63 67 134 64 67 106 65 68 127 66 66 121 67 71 150 68 64 116 69 67 125 70 69 131 71 69 129 72 66 129 73 70 148 74 68 105 75 68 110 76 69 118 77 68 122 78 65 124 79 69 135 80 65 116 81 68 125 82 69 133 83 67 138 84 70 124 85 69 136 86 65 115 87 69 132 88 68 143 89 65 134 90 63 122 91 70 153 92 68 126 93 68 134 94 67 134 95 66 118 96 69 121 97 65 132 98 66 139 99 67 110 100 70 154Explanation / Answer
the simple linear model is given by the equation
y= a + bx + e
where the y- weight
a - intercept
b- slope
e - error
insert data in excel and calculate the regression, path is
data analysis > regression >
enter data
output is
ANOVA
df
SS
MS
F
Significance F
Regression
1
2219.272
2219.272
19.18876
2.97E-05
Residual
98
11334.17
115.6548
Total
99
13553.44
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
-40.86852037
38.30037
-1.06705
0.28857
-116.874
35.13732
-116.874
35.13732
height (inches)
2.481629482
0.566518
4.380497
2.97E-05
1.357393
3.605865
1.357393
3.605865
the predicted regression equation is,
y=-40.86 + 2.48 y ............................................................predicted regression model
Regression Statistics
Multiple R
0.404650853
R Square
0.163742313
Adjusted R Square
0.155209071
Standard Error
10.75429121
Observations
100
r is 0.40 so there is low positive correlation between the two varible.
strength- R-equare value is 0.16 , so there is very very less prediction aveliable from the independent variable.
thanks
ANOVA
df
SS
MS
F
Significance F
Regression
1
2219.272
2219.272
19.18876
2.97E-05
Residual
98
11334.17
115.6548
Total
99
13553.44
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
-40.86852037
38.30037
-1.06705
0.28857
-116.874
35.13732
-116.874
35.13732
height (inches)
2.481629482
0.566518
4.380497
2.97E-05
1.357393
3.605865
1.357393
3.605865
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