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 (a) Write down the regression model. (b) Interpret the regression coefficient for the fitted model. (e) For these data, n = 30, S759.8148, 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.).

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Author:Amos Gilat
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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
(a) Write down the regression model.
(b) Interpret the regression coefficient for the fitted model.
(c)
For these data, n = 30, S = 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.).
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 (a) Write down the regression model. (b) Interpret the regression coefficient for the fitted model. (c) For these data, n = 30, S = 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.).
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