Least squares regression and residuals Quiz

1. $S_{xx}=20$ and $S_{xy}=50$. Find the gradient of the regression line of $y$ on $x$.

• A. $2.5$
• B. $0.4$
• C. $1000$
• D. $30$

2. $\bar x=4$, $\bar y=10$ and $b=2$. Find $a$.

• A. $18$
• B. $2$
• C. $8$
• D. $-2$

3. The regression line predicts $\hat y=23$ for an observation with $y=20$. Find the residual.

• A. $3$
• B. $0.87$
• C. $43$
• D. $-3$

4. $S_{yy}=50$, $S_{xy}=20$ and $S_{xx}=10$. Find the residual sum of squares.

• A. $40$
• B. $20$
• C. $10$
• D. $30$

5. A data set has regression line $y=3+2x$ for $x$ from 1 to 7. Which statement about predicting $y$ at $x=30$ is correct?

• A. It is reliable because the line is least squares
• B. It is extrapolation and may be unreliable
• C. It is interpolation
• D. It is reliable if the RSS is small