Consider the following set of data.

$x$x |
$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 |
---|---|---|---|---|---|---|---|---|---|---|

$y$y |
$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.

Give your answer to two decimal places.

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`=`a``x`+`b`. Give all values to one decimal place.

Easy

Approx 5 minutes

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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.

Investigate bivariate measurement data