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Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.1: Functions Of Several Variables
Problem 34E: The following table provides values of the function f(x,y). However, because of potential; errors in...
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Given are five observations for two variables, and y.
The estimated regression equation is ŷ = 0.2 +2.6x
a. Compute the mean square error using the following equation (to 3 decimals).
0.643
d. Use the t test to test the following hypotheses (α = 0.05 ):
Ho B₁ = 0
:
Ha B₁ 0
Compute the value of the t test statistic (to 2 decimals).
4.133
b. Compute the standard error of the estimate using the following equation (to 3 decimals).
Use Table 2 of Appendix B to find the p-value.
The p-value is between 0.025 and 0.05 ✓
What is your conclusion?
2.033
c. Compute the estimated standard deviation by using the following equation (to 3 decimals).
Regression
Source of Variation Degrees of Freedom Sum of Squares Mean Square
Error
X;
Total
Yi
X
X
1
X
3
Conclude a significant relationship exists between and y
e. Use the F test to test the hypotheses in part (d) at a 0.05 level of significance. Present the results in the analysis of variance table format.
Complete the F table below. Give the Sum of Squares to 1 decimal, the Mean Squares to 3 decimals, F ratio to 2 decimals and the p-value to 4 decimals. Do not round intermediate calculations.
2 3
7
5
F
4 5
11 14
p-value
Transcribed Image Text:Given are five observations for two variables, and y. The estimated regression equation is ŷ = 0.2 +2.6x a. Compute the mean square error using the following equation (to 3 decimals). 0.643 d. Use the t test to test the following hypotheses (α = 0.05 ): Ho B₁ = 0 : Ha B₁ 0 Compute the value of the t test statistic (to 2 decimals). 4.133 b. Compute the standard error of the estimate using the following equation (to 3 decimals). Use Table 2 of Appendix B to find the p-value. The p-value is between 0.025 and 0.05 ✓ What is your conclusion? 2.033 c. Compute the estimated standard deviation by using the following equation (to 3 decimals). Regression Source of Variation Degrees of Freedom Sum of Squares Mean Square Error X; Total Yi X X 1 X 3 Conclude a significant relationship exists between and y e. Use the F test to test the hypotheses in part (d) at a 0.05 level of significance. Present the results in the analysis of variance table format. Complete the F table below. Give the Sum of Squares to 1 decimal, the Mean Squares to 3 decimals, F ratio to 2 decimals and the p-value to 4 decimals. Do not round intermediate calculations. 2 3 7 5 F 4 5 11 14 p-value
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