Correlation Basics
Estimate & Describe Correlations
Regression Lines
Residuals
r^2 and s
100
What letter represents the correlation coefficient
"r"
100
Is the relationship in the scatterplot positive or negative?
Positive
100
What are the slope and y-intercept in the following regression line equation?
ŷ = 102.87 + 2.6x
slope: 2.6
y-int: 102.87
100
How do you calculate the residual?
residual = observed y - predicted ŷ
100
What does the standard deviation of residuals (s) measure?
how much the observed values vary, on average, from the values predicted by the least-squares regression line.
200
How many variables are involved with correlation?
Two
200
Describe a correlation of r = 0.243
positive and weak
200
Assuming that x and y show a correlation, would the relationship modeled by the regression line ŷ = -23 + 9.2x be a positive or negative?
positive, because there is a positive slope in the regression line.
200
Finish the sentence:
The residual is negative when...
The predicted value for y overestimates the observed value. OR
The observed value for y is less than the predicted value.
200
The scatterplot shows the hand span (in centimeters) and number of Starburst candies grabbed by different students, along with the regression line. For this model, s = 4.03. Interpret s in context.
The actual number of Starburst candies grabbed is typically about 4.03 away from the number predicted by the least-squares regression line.
300
True or False if the correlation coefficient "r" is negative (ex: -0.67) there is no correlation.
False
300
Describe a correlation of r = -0.678
negative and strong
300
Using the equation ŷ = 1.65 - 0.02x, find the predicted value of y when x = 5.
ŷ = 1.55
300
Calculate the residual if y = 45 and ŷ = 42
3
300
The scatterplot shows the hand span (in centimeters) and number of Starburst candies grabbed by different students, along with the regression line. For this model, r^2 = 0.697. Interpret r^2 in context.
About 69.7% of the variability in number of Starburst candies grabbed is accounted for by variability in hand size.
400
Come up with a real world example of positive correlation.
...
400
Describe the correlation shown in the scatterplot.
positive and weak to moderate
400
The relationship between NFL teams' salary and number of wins in a season can be predicted using the relationship
ŷ = 5 + 0.134 x
where x = teams salary in millions, and ŷ = predicted wins. Interpret the slope in context.
for every 1 million dollars in salary, the team wins increase by 0.134
400
Interpret a residual of -2.3
The observed value of the response variable was 2.3 units less than the predicted value.
400
If the correlation coefficient is r= 0.84 what is the percent of variation in the response variable?
0.71 or 71%
500
Come up with a real world example of negative correlation.
...
500
Estimate the correlation for the scatterplot below.
r = -0.7 to -0.9
500
ŷ = -29.8 + 2.83x measures the amount of Starburst candies someone can hold based on their hand span measured in cm.
Interpret the y-intercept. Does it make sense in context?
Someone with a hand length of 0 cm can hold -29.8 Starburst candies.
This does not make sense in context because you cannot have 0 cm hand length, and someone cannot hold negative candies.
500
ŷ = -29.8 + 2.83x measures the amount of Starburst candies someone can hold based on their hand span measured in cm. Find and interpret the residual for Andre, who has a hand span of 22 cm and grabbed 36 Starburst candies.
Andre grabbed 3.54 more Starburst candies than the number predicted by the regression line.
500
If the correlation coefficient is r= -0.7 what is the percent of variation in the response variable?
0.49 or 49%