Question

A study was made on the effect of temperature on the yield of a chemical process. The following data (in coded form) were collected. x: -5 -4 -3 -2 -1 0 1 2 3 4 5 y: 1 5 4 7 10 8 9 13 14 13 8 Linear regression model $y = \beta_0 + \beta_1 x + e$ is fitted for the above data. (a) Describe the parameters and variables in the model. (b) Obtain the least squares estimates of $\beta_0$ and $\beta_1$ and hence the prediction equation. (c) Construct ANOVA table and test $H_0: \beta_1 = 0$ at 5% level of significance. (d) What are 95% confidence limits for $\beta_1$? (e) What are the confidence limits for the true mean value of y when x = 3 at 95% confidence level? (f) Are there any indications that a better model can be tried?

          A study was made on the effect of temperature on the yield of a chemical process. The following data (in
coded form) were collected.
x: -5 -4 -3 -2 -1 0 1 2 3 4 5
y: 1 5 4 7 10 8 9 13 14 13 8
Linear regression model $y = \beta_0 + \beta_1 x + e$ is fitted for the above data.
(a) Describe the parameters and variables in the model.
(b) Obtain the least squares estimates of $\beta_0$ and $\beta_1$ and hence the prediction equation.
(c) Construct ANOVA table and test $H_0: \beta_1 = 0$ at 5% level of significance.
(d) What are 95% confidence limits for $\beta_1$?
(e) What are the confidence limits for the true mean value of y when x = 3 at 95% confidence level?
(f) Are there any indications that a better model can be tried?

$A study was made on the effect of temperature on the yield of a chemical process. The following data (in coded form) were collected. x: -5 -4 -3 -2 -1 0 1 2 3 4 5 y: 1 5 4 7 10 8 9 13 14 13 8 Linear regression model y = β0 + β1 x + e is fitted for the above data. (a) Describe the parameters and variables in the model. (b) Obtain the least squares estimates of β0 and β1 and hence the prediction equation. (c) Construct ANOVA table and test H0: β1 = 0 at 5% level of significance. (d) What are 95% confidence limits for $\beta1$? (e) What are the confidence limits for the true mean value of y when x = 3 at 95% confidence level? (f) Are there any indications that a better model can be tried?$

Added by Richard W.

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