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(b) Interpret the regression coefficient for the fitted model.

(b) Interpret the regression coefficient for the fitted model.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Q12 d

The yield of a chemical reaction is influenced by the temperature at which the reaction is run. A certain type of reaction was run 30 times, at different temperatures (in Celsius), and the yield of the product (in % area) was recorded. A simple linear regression model was fitted to these data, where the yield is the response variable, and the temperature is the explanatory variable. The coefficients table from the output produced when fitting the simple linear regression model in Minitab is given below. Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 0.52 1.29 0.40 0.689 x 0.474 0.170 2.78 0.010 1.00 (b) Interpret the regression coefficient for the fitted model. (c) For these data, n = 30, S₂ = 759.8148, and s=4.69245. Show that a 95% confidence interval for 3, the regression coefficient, is given by (0.125, 0.823) (rounded to 3 d.p.). | (d) From the Minitab output, the p-value for the two-sided t-test with null hypothesis Ho: 3=0 is less than 0.05. Did you expect this from the confidence interval? Explain why, or why not.
Transcribed Image Text:The yield of a chemical reaction is influenced by the temperature at which the reaction is run. A certain type of reaction was run 30 times, at different temperatures (in Celsius), and the yield of the product (in % area) was recorded. A simple linear regression model was fitted to these data, where the yield is the response variable, and the temperature is the explanatory variable. The coefficients table from the output produced when fitting the simple linear regression model in Minitab is given below. Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 0.52 1.29 0.40 0.689 x 0.474 0.170 2.78 0.010 1.00 (b) Interpret the regression coefficient for the fitted model. (c) For these data, n = 30, S₂ = 759.8148, and s=4.69245. Show that a 95% confidence interval for 3, the regression coefficient, is given by (0.125, 0.823) (rounded to 3 d.p.). | (d) From the Minitab output, the p-value for the two-sided t-test with null hypothesis Ho: 3=0 is less than 0.05. Did you expect this from the confidence interval? Explain why, or why not.
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