New Zealand
Level 8 - NCEA Level 3

# Interpreting Information from Fitted Lines

## Interactive practice questions

A least squares regression line is given by $y=3.59x+6.72$y=3.59x+6.72.

a

State the gradient of the line.

b

Which of the following is true?

The gradient of the line indicates that the bivariate data set has a positive correlation.

A

The gradient of the line indicates that the bivariate data set has a negative correlation.

B

The gradient of the line indicates that the bivariate data set has a positive correlation.

A

The gradient of the line indicates that the bivariate data set has a negative correlation.

B
c

Which of the following is true?

If $x$x increases by $1$1 unit, then $y$y increases by $3.59$3.59 units.

A

If $x$x increases by $1$1 unit, then $y$y decreases by $3.59$3.59 units.

B

If $x$x increases by $1$1 unit, then $y$y decreases by $6.72$6.72 units.

C

If $x$x increases by $1$1 unit, then $y$y increases by $6.72$6.72 units.

D

If $x$x increases by $1$1 unit, then $y$y increases by $3.59$3.59 units.

A

If $x$x increases by $1$1 unit, then $y$y decreases by $3.59$3.59 units.

B

If $x$x increases by $1$1 unit, then $y$y decreases by $6.72$6.72 units.

C

If $x$x increases by $1$1 unit, then $y$y increases by $6.72$6.72 units.

D
d

State the value of the $y$y-intercept.

Easy
Approx a minute

A least squares regression line is given by $y=-3.67x+8.42$y=3.67x+8.42.

The following scattergraph shows the value of various $4$4 bedroom, $2$2 bathroom homes in a new suburb.

The price of various second-hand Mitsubishi Lancers are shown below.

### 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.

#### 91582

Use statistical methods to make a formal inference