Pack A — Fluency

Mathematics

Year 10 · Bivariate Statistics

Pack A · Fluency

Name: _________________________________

Date: _________________ Class: ___________

Answer all questions. Show your working. Questions are grouped by challenge level.

BronzeQuestions 1–10

1.
A scatter plot shows that as $x$ increases, $y$ tends to $increase$ . Describe the correlation.
2.
A scatter plot shows random points with no clear trend. Describe the correlation.
3.
Points lie tightly along a straight line going up. Describe the strength and direction of correlation.
4.
A study plots height (cm) against weight (kg). Which is the (a) independent variable and (b) dependent variable, by convention if predicting weight?
5.
A graph shows hours of sunshine vs ice cream sales. The points trend upward. Describe the relationship.
6.
A line of best fit has equation $y = 3x + 2$ . Predict $y$ when $x = 5$ .
7.
A line of best fit has equation $y = 4x + 7$ . State the gradient and $y$ -intercept.
8.
A study finds a positive correlation between ice cream sales and shark attacks. Does eating ice cream cause shark attacks?
9.
In a scatter of test scores vs revision hours, one point sits well above the line of best fit. What does this represent?
10.
A regression line of $y$ on $x$ is $y = 0.8 x + 5$ . Predict $y$ for $x = 20$ .

SilverQuestions 11–20

11.
A line of best fit passes through $(0, 3)$ and $(5, 18)$ . Find its equation.
12.
A regression line for height ( $y$ , cm) on age ( $x$ , years) is $y = 6x + 70$ . Predict the height of a 9-year-old.
13.
A regression line of test mark ( $y$ ) on hours of revision ( $x$ ) is $y = 5x + 40$ . Interpret the gradient in context.
14.
A regression line of test mark ( $y$ ) on hours of revision ( $x$ ) is $y = 5x + 40$ . Interpret the $y$ -intercept in context.
15.
For each correlation coefficient $r$ , describe the correlation. $r = 0.85$ .
16.
A line of best fit is $y = 4x + 6$ . Find $x$ when $y = 30$ .
17.
A regression line of $y$ on $x$ passes through the mean point $(\bar{x}, \bar{y})$ . If $\bar{x} = 5$ and the line is $y = 3x + 4$ , find $\bar{y}$ .
18.
A regression equation was fitted using $x$ -values from 5 to 20. Using the line, $y$ is predicted for $x = 10$ (case A) and $x = 30$ (case B). Which is interpolation, which is extrapolation?
19.
Plot 1 has $r = 0.9$ and Plot 2 has $r = 0.2$ . Which shows a stronger linear relationship?
20.
A scatter plot of time spent gaming vs test scores has line of best fit $y = -2x + 70$ . Interpret in context.

GoldQuestions 21–30

21.
Five data points: (1, 3), (2, 5), (3, 7), (4, 9), (5, 11). Find the regression line by inspection.
22.
A regression line $y = 0.5x + 20$ was fitted to $x$ -values from 10 to 50. (a) Predict $y$ at $x = 30$ . (b) At $x = 80$ the prediction would be?
23.
A car's mileage (km) vs its resale value (£). Suggested data has $r \approx -0.92$ . Interpret.
24.
A regression line has a strong outlier. Will removing it (a) increase or decrease $|r|$ ? (b) Why?
25.
Five data points: $\bar{x} = 5, \bar{y} = 12$ ; regression line has gradient $2$ . State the regression equation.
26.
Categorise the correlation based on $r$ : (a) $r = 0.3$ , (b) $r = 0.7$ , (c) $r = -0.95$ , (d) $r = 0.05$ .
27.
Five data points have $\bar{x} = 4$ and $\bar{y} = 11$ . Four are $(2, 7), (3, 9), (5, 13), (6, 15)$ . Find the fifth.
28.
Studies find $r = 0.9$ between countries' chocolate consumption and number of Nobel Prize winners. Does eating chocolate cause Nobel Prizes?
29.
LOBF $y = 2x + 1$ predicts $y$ at $x = 5$ . Actual measured value is 9. What is the residual?
30.
A regression line predicts temperature in °C from altitude (m): $T = -0.006a + 15$ . Predict $T$ at altitude 2000 m.

PlatinumQuestions 31–40

31.
A regression has $r = 0.8$ . What proportion of variation in $y$ is explained by $x$ ?
32.
Two studies of " $y$ vs $x$ " have regression lines: Study A: $y = 3x + 5$ , $r = 0.6$ . Study B: $y = 3x + 5$ , $r = 0.9$ . Which is a better fit? Why?
33.
A regression line $y = 2x + 5$ has $r^2 = 0.7$ . At $x = 10$ , you predict $y = 25$ . What does $r^2 = 0.7$ tell you?
34.
Three points and their LOBF predictions: $(1, 4) \to$ predicted 3.5; $(2, 6) \to$ predicted 5.5; $(3, 8) \to$ predicted 7.5. Find the sum of residuals.
35.
Five students rank their preference for two subjects. The rank correlation is 0.8. Interpret.
36.
A scatter plot looks like a U-shape. A student fits a straight LOBF and finds $r = 0$ . What does this tell us about the relationship?
37.
A regression line of "ice cream sales" on "temperature (°C)" gives $y = 2.5x + 5$ for $x$ in $[15, 35]$ . At $x = -10$ °C, the prediction is $-20$ . Comment.
38.
A dataset has $r = -0.7$ and $r^2 = 0.49$ . Write a one-sentence summary for a non-technical audience.
39.
For a sample of cars, fuel economy ( $y$ , mpg) vs engine size ( $x$ , L) gives $y = -8x + 50$ . (a) Predict mpg for a 2 L engine. (b) Comment on $x = 5$ L.
40.
A study finds $r = 0.95$ between heights of parent and child. Does this mean a tall parent guarantees a tall child?