WACE Mathematics Applications bivariate data and time series: exam-style practice quiz

Question 1

A scatterplot of the age of a car (years) against its resale value (dollars) for 40 cars has $r = -0.78$. Which description is correct?

Accepted Answer

A strong negative linear association: older cars tend to have lower resale values

Question 2

For data on daily hours of sunshine and daily electricity generated by a household's solar panels, $r = 0.9$. Which statement about the coefficient of determination is correct?

Accepted Answer

About 81 percent of the variation in electricity generated is explained by the variation in hours of sunshine

Question 3

A researcher wants to predict a person's reaction time from the number of hours they slept the night before. Which is the correct choice of variables?

Accepted Answer

Reaction time is the response variable and hours slept is the explanatory variable

Question 4

For a delivery van, the least-squares line relating fuel used $F$ (litres) to distance travelled $d$ (km) is $F = 2.1 + 0.075d$. The best interpretation of the slope is:

Accepted Answer

On average, each additional kilometre travelled is associated with an extra 0.075 litres of fuel used

Question 5

Using $F = 2.1 + 0.075d$, a 200 km trip actually used 17.5 litres. The residual for this trip is:

Accepted Answer

0.4 litres

Question 6

A least-squares line has $r = 0.93$, but its residual plot shows a clear U-shaped pattern. What should you conclude?

Accepted Answer

The relationship is non-linear, so a linear model is not the best choice despite the high r

Question 7

A least-squares line relating tree height to age was fitted to trees aged 5 to 40 years, with $r = 0.95$. For which age is a prediction most reliable?

Accepted Answer

20 years

Question 8

Across 50 Australian towns there is a strong positive association between the number of cafes and the number of car accidents each year. Which is the most reasonable explanation?

Accepted Answer

Town population is a confounding variable that tends to increase both quantities

Question 9

Quarterly sales (in thousands) are Q1 12, Q2 18, Q3 26, Q4 16 and then Q1 14. The centred four-point moving average for Q3 is:

Accepted Answer

18.25

Question 10

The seasonal index for the fourth quarter of a shop's sales is 1.3. This means:

Accepted Answer

Fourth-quarter sales are typically 30 percent above the quarterly average

Question 11

A business has quarterly seasonal indices of 0.85 for Q1, 1.10 for Q2 and 1.20 for Q3. The seasonal index for Q4 is:

Accepted Answer

0.85

Question 12

A trend line fitted to deseasonalised quarterly sales is $y = 250 + 12t$ , where $t = 1$ is the first quarter of the data. The value $t = 17$ is a Q1, and the Q1 seasonal index is 0.9. The forecast of actual sales for $t = 17$ is closest to:

Accepted Answer

408.6