Find the confidence interval for the expected value of y

Assignment Help Engineering Mathematics

Reference no: EM131404562

(a) Eight experiments were carried out a various condition of Saturation (X₁) and Transisomers (X₂). The values of the response Y are listed below together with the corresponding levels of X₁ and X₂.

y_i	Saturation x_i1	Transisomers x_i2
66.0	38	47.5
43.0	41	21.3
36.0	34	36.5
23.0	35	18.0
22.0	31	29.5
14.0	34	14.2
12.0	29	21.0
7.6	32	10.0

Some results from fitting a linear model to this data set are given below.

Estimates:	(Intercept) -94.552	X1 2.802	X2 1.073
Var-cov:	(Intercept)	X₁	X₂
(Intercept)	99.270	-2.910	0.056
X₁	-2.910	0.091	-0.008
X₂	0.56	-0.008	0.009

(i) Using a significance level of 5%, test whether the two regressors Saturation and Transisomers have the same effect on the response.

(ii) Find the 95% confidence interval for the expected value of Y corresponding to X₁ = 30 and X₂ = 15.

(b) Suppose that a regression model with two regressors X1 and X2 which have been centred is being fitted. Show that

where ρ is the correlation coefficient between X₁ and X₂ and S_{X_iX_j} is the corrected sum of products (or squares if i = j) of X_i and X_j.

(c) Use the result in part (d) to find the variance inflation factors of the least squares estimates of the regression coefficients, b^{^}₁ and b^{^}₂, and show that the standard errors of b^{^}₁ and b^{^}₂ tend to infinity as ρ tends to -1 or 1. What does this indicate about regression analysis if there is collinearity?

Reference no: EM131404562

Questions Cloud

Discuss any potential ethical or social responsible issues : Select/ identify a major consumer product and the company that makes it. Provide a brief history of them both. (Select an existing publicly owned company. View the link Public Companies for a comprehensive list of publicly traded companies.)Identi..

Determine nature of the relationship between two variables : Sometimes the main purpose of a regression analysis is to determine the nature of the relationship between two variables, and sometimes the main purpose is to use the equation in the future to predict a y value when the x value is known.

Determine the payback period for each site : Using a discount rate of 8% calculate the net present value for each site.

Sketch a scatterplot with an outlier : Sketch a scatterplot with an outlier that would inflate the correlation between the two variables. Sketch a scatterplot with an outlier that would deflate the correlation between the two variables.

Find the confidence interval for the expected value of y : Using a significance level of 5%, test whether the two regressors Saturation and Transisomers have the same effect on the response. Find the 95% confidence interval for the expected value of Y corresponding to X1 = 30 and X2 = 15

What would you suggest as a name for the entire procedure : Suppose the statistics community is having a contest to rename regression to something more descriptive of what it actually does. What would you suggest as a name for the entire procedure? As a name for the regression line?

Identify the payback period for each option : Calculate the net present value of each options using a discount rate of 12%.

How you use your scatterplot to help you make prediction : What other variables, aside from her mother's height, might be useful for improving your prediction? How could you use these variables in conjunction with the mother's height?

What is an example of two variables that have no association : Explain what it means when two variables have a negative association. What is an example of two variables that would have no association?

User Account

All Pages