Question

True/False, & explain why in one or two sentences:

4. In the equation c = α + i + u, c denotes consumption and i denotes income. The residual for the 5th observation if c5 =$865 and ^c5 =$890 is 20.

5. The sum of squared residuals (SSR) in a regression analysis is 623.5 and the total sum of squares (SST) is equal to 751.85. The R2 is therefore equal to 0.24.

6. The value of R2 always lies between 0 and 1.

Answer 1

Answer 2

Question 4:

Statement: In the equation $c=\alpha +i+u$, $c$ denotes consumption and $i$ denotes income. The residual for the 5th observation if $c_5=\mathrm{\$}865$ and ${\widehat{c}}_5=\mathrm{\$}890$ is 20.

Answer: False

Explanation:
The residual is calculated as $e=\text{actual value}-\text{predicted value}=c_5-{\widehat{c}}_5=865-890=-25$, not 20.

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Question 5:

Statement: The sum of squared residuals (SSR) in a regression analysis is 623.5 and the total sum of squares (SST) is equal to 751.85. The $R^2$ is therefore equal to 0.24.

Answer: False

Explanation:
$R^2$ is calculated as $1-\frac{\text{SSR}}{\text{SST}}=1-\frac{623.5}{751.85}\approx 0.17$, not 0.24.

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Question 6:

Statement: The value of $R^2$ always lies between 0 and 1.

Answer: True

Explanation:
$R^2$ represents the proportion of variance in the dependent variable explained by the model, so it is bounded between 0 (no explanation) and 1 (perfect fit).