r runs from −1 to 1: its sign gives the direction and its size the strength of a straight-line relationship. Squaring it gives the share of the variation in y that the line explains.
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For a set of data, r=0.59 between hours studied and exam score. Find r2 and interpret it in context.r2=0.3481:about 34.81% of the variation in exam score is explained by the linear relationship with hours studied
For a set of data, r=0.48 between age of a child and height of a child. Find r2 and interpret it in context.r2=0.2304:about 23.04% of the variation in height of a child is explained by the linear relationship with age of a child
For a set of data, r=0.55 between tree age and trunk diameter. Find r2 and interpret it in context.r2=0.3025:about 30.25% of the variation in trunk diameter is explained by the linear relationship with tree age
For a set of data, r=0.54 between practice time and free-throw percentage. Find r2 and interpret it in context.r2=0.2916:about 29.16% of the variation in free-throw percentage is explained by the linear relationship with practice time
Which shows the stronger linear relationship, r=0.39or r=0.58? Explain.r=0.58: it is closer to 1
Which shows the stronger linear relationship, r=0.66or r=−0.43? Explain.r=0.66: the size of r, not its sign, gives the strength
Which shows the stronger linear relationship, r=−0.63or r=−0.35? Explain.r=−0.63: it is closer to −1
For a set of data, r=0.72 between height and shoe size. Find r2 and interpret it in context.r2=0.5184:about 51.84% of the variation in shoe size is explained by the linear relationship with height
For a set of data, r=0.38 between daily high temperature and ice cream sales. Find r2 and interpret it in context.r2=0.1444:about 14.44% of the variation in ice cream sales is explained by the linear relationship with daily high temperature
For a set of data, r=0.72 between calories eaten and weight gained. Find r2 and interpret it in context.r2=0.5184:about 51.84% of the variation in weight gained is explained by the linear relationship with calories eaten
For a set of data, r=−0.74 between outdoor temperature and heating bill. Find r2 and interpret it in context.r2=0.5476:about 54.76% of the variation in heating bill is explained by the linear relationship with outdoor temperature
For a set of data, r=−0.94 between car age and car price. Find r2 and interpret it in context.r2=0.8836:about 88.36% of the variation in car price is explained by the linear relationship with car age
For a set of data, r=−0.65 between altitude and air temperature. Find r2 and interpret it in context.r2=0.4225:about 42.25% of the variation in air temperature is explained by the linear relationship with altitude
Which shows the stronger linear relationship, r=−0.87or r=0.32? Explain.r=−0.87: the size of r, not its sign, gives the strength
For a set of data, r=0.37 between floor area and house price. Find r2 and interpret it in context.r2=0.1369:about 13.69% of the variation in house price is explained by the linear relationship with floor area
For a set of data, r=−0.54 between hours of sleep and reaction time. Find r2 and interpret it in context.r2=0.2916:about 29.16% of the variation in reaction time is explained by the linear relationship with hours of sleep
For a set of data, r=−0.5 between hours of TV watched and hours of homework done. Find r2 and interpret it in context.r2=0.25:about 25% of the variation in hours of homework done is explained by the linear relationship with hours of TV watched
For a set of data, r=−0.71 between miles driven and gas left in the tank. Find r2 and interpret it in context.r2=0.5041:about 50.41% of the variation in gas left in the tank is explained by the linear relationship with miles driven
For a set of data, r=−0.63 between ticket price and tickets sold. Find r2 and interpret it in context.r2=0.3969:about 39.69% of the variation in tickets sold is explained by the linear relationship with ticket price
Which shows the stronger linear relationship, r=0.69or r=0.32? Explain.r=0.69: it is closer to 1
r=0.8. What percent of the variation in y is explained?
r² = 0.64.
The answer is 64%.
Where students go wrong
Reading a strong r as a steep line. r measures how tightly the points hug the line, not the slope: a nearly flat line can have r close to 1.
Also called correlation coefficient r, r squared or coefficient of determination.
Questions about these worksheets
Yes. Every correlation coefficient sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Statistics is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the correlation coefficient questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
Reading a strong r as a steep line. r measures how tightly the points hug the line, not the slope: a nearly flat line can have r close to 1.