You wish to explore the relationship between two variables, X and Y, for 17 pati

Question

You wish to explore the relationship between two variables, X and Y, for 17 patients for purposes of predicting the value of Y, given the value of X. In order (from patient 1 through patient 17), their corresponding values for X are: 9, 15, 10, 16, 10, 20, 11, 20, 15, 15, 8, 13, 18, 10, 8, 10, 16 and the matching (corresponding) values of Y: 45, 57, 45, 51, 65, 88, 44, 87, 89, 59, 66, 65, 56, 47, 66, 41, 56. Given this information, calculate the standard error of the estimate. Assume an alpha of 0.05. Provide your answer with a level of accuracy of 2 decimal places.
You wish to explore the relationship between two variables, X and Y, for 17 patients for purposes of predicting the value of Y, given the value of X. In order (from patient 1 through patient 17), their corresponding values for X are: 9, 15, 10, 16, 10, 20, 11, 20, 15, 15, 8, 13, 18, 10, 8, 10, 16 and the matching (corresponding) values of Y: 45, 57, 45, 51, 65, 88, 44, 87, 89, 59, 66, 65, 56, 47, 66, 41, 56. Given this information, calculate the standard error of the estimate. Assume an alpha of 0.05. Provide your answer with a level of accuracy of 2 decimal places.
You wish to explore the relationship between two variables, X and Y, for 17 patients for purposes of predicting the value of Y, given the value of X. In order (from patient 1 through patient 17), their corresponding values for X are: 9, 15, 10, 16, 10, 20, 11, 20, 15, 15, 8, 13, 18, 10, 8, 10, 16 and the matching (corresponding) values of Y: 45, 57, 45, 51, 65, 88, 44, 87, 89, 59, 66, 65, 56, 47, 66, 41, 56. Given this information, calculate the standard error of the estimate. Assume an alpha of 0.05. Provide your answer with a level of accuracy of 2 decimal places.

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Y
Independent Variable: X
Y = 33.252162 + 2.0612198 X
Sample size: 17
R (correlation coefficient) = 0.5353163
R-sq = 0.28656354
Estimate of error standard deviation: 13.500549

Parameter estimates:

Analysis of variance table for regression model:

Hence,

Standard error of the estimate = 13.50

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 33.252162 11.539153 0 15 2.8816814 0.0114 Slope 2.0612198 0.839742 0 15 2.4545871 0.0268

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