Scatter Plots and Correlation
As points go from left to right, if they generally rise, the correlation is...
Positive
What is slope? Give an interpretation.
How much the line rises for every increase in x. Rise over run.
What is a residual plot that looks like a cloud of points randomly scattered near the horizontal line at zero
Good linear fit, the residuals are low
Out of 240 students surveyed, 96 said they own a dog. What is the proportion who own a dog.
96/240=0.4=40%
What is the one thing correlation NEVER proves.
Causation
The car-insurance scatter plot had r = –0.951. Is this correlation strong or weak?
Very strong (close to –1)
If the correlation is negative, is the number multiplying x in the best fit line positive or negative
Negative (the slope will always be in the same direction as the correlation)
The formula used to calculate a residual.
Actual y - Predicted y
In a two-way table, the ______ is found by dividing a cell by its row or column total.
Relative frequency
Ice cream sales and drowning deaths are positively correlated in summer months. What is the likely lurking (confounding) variable.
The temperature
A hat company finds that the more of a certain type of hat they make, the lower the average price of that type of hat. This is a _____ correlation
Negative
In a scatter plot where x represents hours worked and y represents money made, the line of best fit is y=12x+41. How much money is expected to be made if you work for 8 hours?
96 dollars
A residual of –8 for a data point means this:
The actual value was 8 less than the predicted value
A table shows 60% of males and 60% of females surveyed like pepperoni pizza. What type of association exists between gender and pizza preference.
There is no association
A principal sees a strong positive correlation between number of absences and failing grades, then says “absences cause students to fail.” Why is this claim not justified?
Correlation does not imply causation; there may be lurking variables or the relationship could be reversed
A study of hours studied vs. test score gives r ≈ 0. A reasonable conclusion would be:
There is no correlation between hours studied and test score
In our scatter plot of the number of orange vs. the weight of the box, what does the slope represent?
The average weight of the orange (or similar answer)
A residual plot that forms a U-shape instead of a random cloud: good or bad?
Bad: should be close to 0 line
A survey of 400 people: 120 drink coffee and exercise, 80 drink coffee and do not exercise. What is the proportion of coffee drinkers who exercise.
120/200=0.6=60%
Data reveal a strong positive correlation between the number of storks observed nesting in a European country and its human birth rate over 20 years. Why “storks deliver babies” is nonsense, and the real reason for the pattern.
Both stork nesting and birth rates have declined due to modernization / urbanization / fewer rural buildings, and increase in rural settings
A data set has r = 0.45. Changing from feet to inches for the one of the variables will do this to r:
Nothing: the relationship will stay the same, just changing units
In a scatter plot, the x value represents a student's height and the y value represents a student's weight. The y-intercept was at (0,50). Interpret this value and whether it makes sense.
It is extrapolating the data too far, the y-intercept doesn't make physical sense, a student who is 0 feet tall weights 50 pounds????
The residual plot for a good linear model fit looks like:
Residual points near the horizontal 0 line
A completed two-way table with totals 500 students is said to show no association between wearing glasses and playing a sport. The row percentages for “plays sport” must be what, compared to the row percentages for "doesn't play sport".
The percentages should be approximately the same
Researchers find a strong positive correlation between children’s shoe size and their reading level in elementary school. Explain why larger shoes do not cause better reading.
Age (or maturity/grade level) is a lurking variable that affects both shoe size and reading ability