# Quiz Chapter 06.03: Linear Regression

 MULTIPLE CHOICE TEST LINEAR REGRESSION REGRESSION

1. Given $\left(x_{1},y_{1} \right), \, \left( x_{2}, y_{2} \right), \, ... \, , \, \left( x_{n}, y_{n} \right)$ best fitting data to $y = f (x)$ by least squares requires minimization of

2. The following data

 $x$ $1$ $20$ $30$ $40$ $y$ $1$ $400$ $800$ $1300$

is regressed with least square regression to $y = a_{0} + a_{1}x$. The value of $a_{1}$ is most nearly

3. The following data

 $x$ $1$ $20$ $30$ $40$ $y$ $1$ $400$ $800$ $1300$

is regressed with least square regression to $y = a_{1}x$. The value of $a_{1}$ is most nearly

4. An instructor gives the same $y$ vs $x$ data as given below to four students and asks them to regress the data with least squares regression to $y = a_{0} + a_{1}x$.

 $x$ $1$ $10$ $20$ $30$ $40$ $y$ $1$ $100$ $400$ $600$ $1200$

Each student comes up with four different answers for the straight-line regression model. Only one is correct. The correct model is

5. A torsion spring of a mousetrap is twisted through an angle of $180^{\circ}$. The torque vs. angle data is given below

 Torsion, $T$, N-m $0.110$ $0.189$ $0.230$ $0.250$ Angle, $\theta$, rad $0.10$ $0.50$ $1.1$ $1.5$

The amount of strain energy stored in the mousetrap spring in Joules is

6. A scientist finds that regressing the $y$ vs $x$ data given below to $y = a_{0} + a_{1}x$ results in the coefficient of determination for the straight-line model, $r^{2}$, being zero

 $x$ $1$ $3$ $11$ $17$ $y$ $2$ $6$ $22$ ?

The missing value for $y$ at $x = 17$ most nearly is