Topic 4.4: Correlation and Regression Questions

The table shows the number of hours, x, that six machines have been in use since their last service and the number of parts, y, they produce per hour.

x	2	4	5	7	9	11
y	48	41	40	31	25	18

Write down the value of Pearson's product-moment correlation coefficient, r.

The masses (kg) and lengths (cm) of seven puppies are recorded. The data is (2,30), (3,34), (4,37), (5,41), (6,44), (7,48), (8,52). Find the correlation coefficient r.

For ten pairs of values, a calculator gives $r=0.86$. Describe the correlation.

State the range of possible values for the Pearson correlation coefficient, and what $r=-1$ represents.

A regression line of y on x is y = 0.75x + 6. The mean of x is 12. Find the mean of y.

For ten days, a café records the outside temperature $x$ (°C) and the number of hot drinks sold, $y$. Pearson's correlation coefficient is $r=-0.87$. The thermometer is later found to read $2$°C too low, so $2$ is added to every value of $x$.

State the effect of this change on $r$.

A regression line of y on x is $y=0.75x+6$. The mean of x is 12. Find the mean of y.

A scatter graph shows points loosely scattered with a slight downward trend. State the type of correlation.

Eight students sit two short quizzes. Their scores are shown.

Quiz A, $x$	12	15	9	18	14	20	11	16
Quiz B, $y$	25	29	20	33	31	37	24	28

Find the value of Pearson's correlation coefficient, $r$, for these scores.

The age and value of six used cars of the same model are shown.

Age, $x$ (years)	1	2	3	5	6	8
Value, $y$ (\$1000s)	18.5	16.0	14.2	11.1	9.8	6.9

Write down the value of Pearson's correlation coefficient, $r$.

For ten pairs of values, a calculator gives r = 0.86. Describe the correlation.

Eight students' daily screen time and test scores give $r=-0.45$. Describe the correlation.

For twelve pairs of values a calculator gives $r=0.91$. Describe the correlation.

Sketch the regression line on the diagram.

Sketch the regression line of $y$ on $x$ on the scatter diagram.

A shop records the hours of sunshine and the number of ice lollies sold on seven days.

Sunshine, $x$ (hours)	3	5	6	8	9	11	12
Lollies sold, $y$	22	30	27	41	38	50	49

Find Pearson's product-moment correlation coefficient, $r$.

For a sample of turkeys, the regression line of cooking time $t$ (minutes) on mass $m$ (kg) is $t=38.5m+21.0$. Interpret the value $38.5$ in context.

The height of a seedling is measured at different ages.

Age, $x$ (weeks)	2	4	5	7	9	11	12
Height, $y$ (cm)	3.1	4.0	5.2	5.6	7.1	8.3	8.4

The regression line of $y$ on $x$ is $y=ax+b$. Write down the value of $a$ and the value of $b$.

The regression line of $y$ on $x$ for a set of data is $y=1.85x+4.3$. The mean of the $x$ values is $6$. Show that the mean of the $y$ values is $15.4$.

A café records the daily temperature and the soup it sells.

Temperature, $x$ (°C)	10	14	15	19	22	26	30
Soup sold, $y$ (litres)	62	55	57	47	44	36	31

The regression line of $y$ on $x$ is $y=ax+b$. Write down the value of $a$ and the value of $b$.