Exam Review -- Bivariate Statistics
1.
Draw a scatterplot of the relationship between two quantitative variables that shows a
strong negative correlation.
2.
What physical feature of your graph in #1 indicates that this is a negative correlation?
What physical feature of your graph indicates that this is a strong correlation?
3.
Give a real-world example of two variables that might be related as shown in your graph.
4.
Suppose I find a study that suggests men are more likely to be color-blind. What might
the scatterplot for this data look like?
5.
Explain why the two variables in #4 are both qualitative (categorical) variables, not
quantitative variables.
6.
Use examples to discuss the difference between correlation and causation. Give
examples of situations that might involve lurking variables or reverse causation.
7.
Explain what the null hypothesis says and give a few real-world examples of twovariable situations where the null hypothesis may or may not apply.
8.
Describe how to evaluate the quality of a mathematical model. Identify possible reasons
for rejecting a linear model.
9.
At right is a histogram of the residuals from a
model. Why do we look at this histogram when
evaluating a model? What do you notice here?
10.
It’s important to think about context as you are
looking at a model. This model looks to see if
the amount of money spent in a school district
can predict the district’s MCAS scores. MCAS
scores can’t exceed 100. How does that explain
the shape of this histogram?
11.
What would the null hypothesis say about the connection between school district
spending and MCAS scores? What would the alternate hypothesis say?
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12.
Here is a scatter plot of world population data, along with a residual plot. Why do we
look at the residual plot? What do you notice here?
13.
(Honors) Draw a picture of a scatter plot for two variables that would have a bimodal
distribution of residuals. Explain the connection between the original scatterplot and the
residual plot.
14.
Can the noise of crickets chirping predict the temperature? A model for this data set has
the equation: Temperature F = 3.29 * chirps per second + 25.2. Suppose the crickets are
chirping 15 times a second. Predict the temperature.
15.
In the crickets model, the standard deviation of the residuals is 3.69. Give a 95%
prediction interval for the temperature when the crickets chirp 15 times a second.
16.
Now suppose the temperature is 81 degrees. Predict how fast the crickets are chirping.
17.
In the crickets model, the model’s predicted values go from 72.6 degrees to 91.1 degrees,
while the residuals range from -.9 to 5.0. What does that tell you about the quality of the
model?
18.
(Honors) In the SAT model, you looked at a student’s SAT score as a predictor of
college GPA. Use this equation: GPA = .00338 * math + .63, with the standard deviation
of residuals at .65. According to that model, what is the minimum math SAT score
needed to be 97.5% sure that a student’s GPA will be 2.8 or above? Draw a graph of the
model before you do any computations.