Statistics, STD2 2026 HSC 22

Researchers were interested in whether the critics' scores for movies could be used to predict the general public's scores for movies.

A random sample of movies was selected, and the average score from the critics and the average score from the public were recorded.

A scatterplot of the dataset and the least-squares regression line are shown.

What was the lowest score given by the public for a movie, correct to 1 decimal place? (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
The gradient of the least-squares regression line for the dataset is 0.54.
Interpret the gradient in the context of the dataset. (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
A new data point is included in the dataset. The critics' score is 7.2 and the public's score is 6.
Identify ONE effect this would have on the least-squares regression line. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---

Show Answers Only

a. $6.1$

b. $\text{Interpretation of gradient = 0.54:}$

$\text{For each 1-point increase in the critics’ score, the predicted public’s}$

$\text{score increases by 0.54 points.}$

c. $\text{The new point lies below the LSRL.}$

$\text{Possible effects could include:}$

$\text{- lowering the LSRL at each critic’s score.}$

$\text{- increasing the LSRL gradient (its LHS will be relatively lower than its RHS).}$

Show Worked Solution

a.	$\text{Lowest public score}$	$=\ \text{$y$-value of the lowest plotted point}$
		$=6.1$