Q9. Consider the regression results from the regression of Y against X for 50 observations:

Y = 5.0 - 1.5 X

The standard error of the estimate is 0.40 and the standard error of the coefficient is 0.45. The predicted value of Y if X is 10 is:

A)        10.

B)        20.

C)        -10.

Q10. Consider the regression results from the regression of Y against X for 50 observations:

Y = 5.0 + 1.5 X

The standard error of the coefficient is 0.50 and the standard error of the forecast is 0.52. The 95% confidence interval for the predicted value of Y if X is 10 is:

A)     {19.480 < Y < 20.052}.

B)     {18.980 < Y < 21.019}.

C)     {18.954 < Y < 21.046}.

Q11. 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.

答案和详解如下：

Q9. Consider the regression results from the regression of Y against X for 50 observations:

Y = 5.0 - 1.5 X

The standard error of the estimate is 0.40 and the standard error of the coefficient is 0.45. The predicted value of Y if X is 10 is:

A)        10.

B)        20.

C)        -10.

Correct answer is C)

The predicted value of Y is: Y = 5.0 – [1.5 (10)] = 5.0 – 15 = -10

Q10. Consider the regression results from the regression of Y against X for 50 observations:

Y = 5.0 + 1.5 X

The standard error of the coefficient is 0.50 and the standard error of the forecast is 0.52. The 95% confidence interval for the predicted value of Y if X is 10 is:

A)     {19.480 < Y < 20.052}.

B)     {18.980 < Y < 21.019}.

C)     {18.954 < Y < 21.046}.

Correct answer is C)

The predicted value of Y is: Y = 5.0 + [1.5 (10)] = 5.0 + 15 = 20. The confidence interval is 20 ± 2.011 (0.52) or {18.954 < Y < 21.046}.

Q11. 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.

Correct answer is 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 standard deviation of the prediction is equal to the squared standard error of the estimate multiplied by [1 + (1 / n) + (x − u)²] / [(n − 1)s_x²]^1/2 = 2.02² × [1 + (1 / 24) + (1.0 − 1.1)²] / (23 × 1.1²)^1/2 = 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.

thx

thx