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Vocab
r and R-squared
Interpreting Slope & Y-intercept
Miscellaneous
100
A measure of how far a prediction is from what is actually observed.
What is a residual?
100
Interpret what a correlation coefficient of r = 0.9 means.
What is strong, positive association?
100
y = 1.25x + 10, where x is the amount of fertilizer in mL and y is the height of the plant (cm). Interpret the y-intercept.
When zero mL of fertilizer are used, the plant is expected to be 10 cm tall.
100
Describe the association in the graph comparing temperature and ice cream sales. https://www.mathsisfun.com/data/images/scatter-ice-cream1.gif
positive, linear, strong association with no apparent outliers
200
A unique line that has the smallest possible value for the sum of the squares of the residuals
What is the Least Squares Regression Line (LSRL)?
200
If the correlation coefficient is zero, what does that mean about the association and the LSRL?
There is no association and the LSRL is a horizontal line.
200
y = 1.25x + 10, where x is the amount of fertilizer in mL and y is the height of the plant (cm). Interpret the slope.
For every additional mL of fertilizer used, the height of the plant increases by 1.25 cm.
200

When comparing age and height, Eva calculated R-squared to be 0.76. Write a sentence to explain what R-squared means in this context and provide at least one other factor that can explain the variability in height.

76% of the variability in height can be explained by a linear relationship with age. The other 24% could be explained by genetics, general health, environmental factors, etc.

300
The measure of the strength of the association between two variables.
What is the correlation coefficient (r)?
300
What must be true for the correlation coefficient to be -1?
All of the points are on the LSRL and the slope is negative.
300
Given the interpretations of slope and y-intercept, write the equation of the LSRL: When the length of the paint on a pencil is 0 cm, the weight of the pencil is 2 grams. For every additional cm of paint, the weight of the pencil increases by 1.4 grams.
y = 1.4x + 2
300

No correlation between the variables.   

What is an r of zero?

400
The four categories that are used to describe association.
What is form, direction, strength, and outliers?
400
Given an LSRL of y = -0.5x + 17 and an R-squared value of .68, determine and interpret the correlation coefficient. Round to the nearest hundredth.
What is r = -0.82? This means there is a moderately strong, negative association.
400
y = 0.41x -14 where x is temperature (degrees F) and y is the number of people at the park (in 1000s). Interpret the y-intercept.
When the temperature is 0 degrees Fahrenheit, there are -14000 people in the park. (Doesn't make sense)
500
y = 1.25x + 10, where x is the amount of fertilizer in mL and y is the height of the plant (cm). r = 0.92 Determine and interpret R-squared.
What is R-squared = 0.8464 About 85% of the variability in plant height can be explained by a linear relationship with the amount of fertilizer used.
500
y = 0.41x -14 where x is temperature (degrees F) and y is the number of people at the park (in 1000s). Interpret the slope.
For every additional degree F in temperature, the number of people at the park increases by 410. When the temperature increases by 1 degree F, the number of people at the park increases by 410.