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6.09 Linear regressions and residual plots

Interactive practice questions

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
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
5min

Consider the following set of data.

Easy
5min

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.

Easy
7min

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

Easy
7min
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Outcomes

I.S.ID.6.b

Informally assess the fit of a function by plotting and analyzing residuals.

I.S.ID.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

I.S.ID.8

Compute (using technology) and interpret the correlation coefficient of a linear fit.

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