A variable Y is regressed against a single variable X across 24 observations. The value of the slope is 1.14, and the constant is 1.3. The mean value of X is 1.10, and the mean value of Y is 2.67. The standard deviation of the X variable is 1.10, and the standard deviation of the Y variable is 2.46. The sum of squared errors is 89.7. For an X value of 1.0, what is the 95% confidence interval for the Y value?
A. 1.68 to 6.56.
B. 1.83 to 6.72.
C. 0.59 to 4.30.solution：B

First the standard error of the estimate must be calculated—it is equal to the square root of the mean squared error, which is equal to the sum of squared errors divided by the number of observations minus 2 = (89.7 / 22)1/2 = 2.02. The variance of the prediction is equal to:

= 2.06

The prediction value is 1.3 + (1.0 × 1.14) = 2.44. The t-value for 22 degrees of freedom is 2.074. The endpoints of the interval are 2.44 ± 2.074 × 2.06 = −1.83 and 6.72.