Question

Consider the following set of ordered pairs shown below. Assuming that the regression equation is

y
^
​
=1.504+0.788x and the SSE =3.81, construct a 90% confidence interval for x=1. Click the icon to view a portion of the Student's t-distribution table. Calculate the upper and lower limits of the confidence interval.
UCL=
LCL=
​
(Round to three decimal places as needed.)

Answer 1

To construct a 90% confidence interval for a given value of x using the regression equation, we need to calculate the point estimate and the error bound for the mean (EBM). The information provided is not sufficient to calculate the EBM, as additional details such as the sample size, critical t-value, and standard error of the estimate are required.

Step-by-step explanation:

The student is asking to construct a 90% confidence interval for the predicted value of y when x=1 using the given regression equation y = 1.504 + 0.788x and the Sum of Squares due to Error (SSE) of 3.81. To find the confidence interval, we would typically use the formula:

• (lower bound, upper bound) = (point estimate − EBM, point estimate + EBM)

Where EBM is the error bound for the mean, and the point estimate is the predicted value of y at x=1, which is:

1.504 + 0.788(1) = 2.292

However, without additional information such as the sample size, the critical t-value for the 90% confidence level, and the standard error of the estimate (which can be calculated from the SSE if the degrees of freedom are known), it is not possible to calculate the Error Bound on the Mean (EBM) and construct the confidence interval. Therefore, the detailed steps to calculate the confidence interval are incomplete and the question cannot be fully answered.