New Zealand
Level 8 - NCEA Level 3

# Least-Squares Lines and Making Predictions

## Interactive practice questions

Consider the following set of data.

 $x$x $y$y $15.7$15.7 $13.1$13.1 $16.1$16.1 $11$11 $18.6$18.6 $15.8$15.8 $12.7$12.7 $12.8$12.8 $14.3$14.3 $16.8$16.8 $28.3$28.3 $28.8$28.8 $28.4$28.4 $29$29 $27.9$27.9 $28.4$28.4 $28.5$28.5 $29$29 $28.5$28.5 $28.6$28.6
a

Using a graphics calculator (or other technology), calculate the correlation coefficient between these scores.

b

Choose the description which best describes the statistical relationship between these two variables.

Strong positive linear relationship

A

Weak relationship

B

Moderate negative linear relationship

C

Moderate positive linear relationship

D

Strong negative linear relationship

E

Strong positive linear relationship

A

Weak relationship

B

Moderate negative linear relationship

C

Moderate positive linear relationship

D

Strong negative linear relationship

E
c

Using a graphics calculator (or other technology), form an equation for the least squares regression line of $y$y on $x$x.

Give your answer in the form $y=ax+b$y=ax+b. Give all values to one decimal place.

Easy
Approx 5 minutes

Consider the following set of data.

The forecast maximum temperature, in degrees Celsius, and the observed maximum temperature are recorded to determine the accuracy in the temperature prediction models used by the weather bureau.

Research on the number of cigarettes smoked during pregnancy and the birth weights of the newborn babies was conducted.

### Outcomes

#### S8-1

Carry out investigations of phenomena, using the statistical enquiry cycle: A conducting experiments using experimental design principles, conducting surveys, and using existing data sets B finding, using, and assessing appropriate models (including linear regression for bivariate data and additive models for time-series data), seeking explanations, and making predictions C using informed contextual knowledge, exploratory data analysis, and statistical inference D communicating findings and evaluating all stages of the cycle.

#### 91581

Investigate bivariate measurement data