Correlation

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#14915

Correlation

$$y=mx+c$$

$$m=r\frac{s_y}{s_x}$$

$$y-intercept = \bar{y}-m\bar{x}$$

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#18614

Research is conducted to determine if there is any relationship between obesity and the number of hours per day children spend in front of a video screen. A group of 13 year old children were surveyed and the average results are tabulated below. Calculate the correlation coefficient and comment on it’s value.

Hours (H)	0.5	1	1.5	2	2.5	3	3.5	4	4.5
Weight above average (W)	0.50	1.00	1.25	1.85	2.20	2.50	3.20	3.40	3.65

enter calculator mode: Mode Stat We need option: A + Bx or 2 variable (depending on your calculator)

enter your first row of data into the x column enter the second row of data into the y column press

Press AC

Press shift 1 [STAT]

select the r option

r = 0.995

since r is almost 1, and positive, then there is a very strong positive correlation between H and W

[Admin]

#18615

The length of a child’s foot increases until they reach adulthood. What is the best description for the relationship between foot length and a child’s age? a. Positive Correlation b. Negaitive Correlation c. Interpoloation d. Extrapoloation
A	positive correlation as as the child’s age increased, their foot length increases as they grow – since age is increasing and length is increasing, then it is positive correlation

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#18617

During a fitness test, the number of sit ups, s, and the number of push ups, p, performed by ten students are recorded. the results are shown in the table. Sit Ups (s) 0 5 15 20 25 30 35 40 45 50 Push Ups (p) 10 15 25 25 33 48 45 50 50 60 a. Calculate the value of the correlation coefficient, r. Give your answer correct to two decimal places. b. Use the formulas to find the gradient and y-intercept of the least squares line of best fit for this data. c. Write the equation of the line of best fit.
a.  enter calculator mode: Mode Stat	to find r we need to enter the values into the calculator – these instructions are for the Casio
We need option: A + Bx	we now need to select regression mode
enter your first row of data into the x column enter the second row of data into the y column	you should see a column for x and one for y, and possible one for freq if you have that turned on (if you do have that column, just ignore it).
press AC	once you have entered all the data, press the AC button, now we need to go get the value of r
press shift 1 [STAT]	we want the option that says Reg, which stands for regression
Select the regression option	you should see a number of choices now, r is the regression, A is the y-intercept and B is the gradient
select the r	pick the r (and don’t forget to press =)
r = 0.97707648	round correct to 2 decimal places
r = 0.98
b.	$$m=r\frac{s_y}{s_x}$$
Shift 1 [STAT] select Var select yσ for sy and press =	we have r so now we need to go get sy and sx back to shift 1, but this time we want the variables
sy = 16.00281225 sx = 15.81929202	shift 1 again and var, and this time we want sx
$$m=0.98\times\frac{16.00281225}{15.81929202}$$ m = 1.0	now we are ready to substitute and find m
back to shift 1 for stat, select var, and find $$\overline{y}$$ and $$\overline{x}$$	y-intercept = $$\overline{y}-m\overline{x}$$
$$\overline{y}$$ = 36.1 $$\overline{x}$$ = 26.5	find the y and x averages
y-intercept = 36.1 – 1 × 26.5 = 9.6	substitute the values into the equation
c. p = s + 9.6	substitute into equation y = mx + c in this case the y will be p and the x will be s

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