1 An experiment involves releasing a coin on a sloping plane so that it slides down the slope and then slides along a horizontal plane at the bottom of the slope before coming to rest. The angle \(\theta ^ { \circ }\) of the sloping plane is varied, and for each value of \(\theta\), the distance \(d \mathrm {~cm}\) the coin slides on the horizontal plane is recorded. A scatter diagram to illustrate the results of the experiment is shown below, together with the least squares regression line of \(d\) on \(\theta\).
\includegraphics[max width=\textwidth, alt={}, center]{28c6a0d9-09a6-4743-af0e-fe2e43e256c9-2_639_972_561_548}

1. State which two of the following correctly describe the variable \(\theta\).

   Controlled variable	Correlation coefficient
   Dependent variable	Independent variable
   Response variable	Regression coefficient

   The least squares regression line of \(d\) on \(\theta\) has equation \(d = 1.96 + 0.11 \theta\).
2. Use the diagram in the Printed Answer Booklet to explain the term "least squares".
3. State what difference, if any, it would make to the equation of the regression line if \(d\) were measured in inches rather than centimetres. ( 1 inch \(\approx 2.54 \mathrm {~cm}\) ).