AP Stats CH 3

Question 1

Interpret a scatter plot (describe a relationship)

Answer 1

Direction(positive/negative/none)
Unusual features (outliers, clusters)
Form (linear or non-linear)
Strength (how close to form)

Question 2

Interpret correlation r

Answer 2

The linear relationship between x and y is “strength” and “direction”

Question 3

Interpret slope

Answer 3

For every “x context”, the
predicted number of “y context”
increases/decreases by “slope”

Question 4

Interpret a residual

Answer 4

The actual “y context” was
“residual” above/below the
predicted value for “x =”

Question 5

Interpret coefficient of determination (r squared)

Answer 5

“Percent” of the variation in “y context” is explained by the linear relationship with “x context”

Question 6

interpret the y intercept

Answer 6

When “x context” is zero, the “y context” is equal to “y intercept”

Question 7

Interpret the standard deviation of the residuals (s)

Answer 7

The actual “y context is
typically about “s” away
from the number predicted by the
LSRL.

Question 8

Desiree is interested to see if students who consume more caffeine tend to study more as
well. She randomly selects 20 students at her school and records their caffeine intake (mg), 𝑥, and the number of hours spent studying, 𝑦. If you were to interpret the scatter plot, what features would you need to include?

Answer 8

Context, direction, form, strength, unusual features

Question 9

Desiree randomly selects 20 students at her school and records their caffeine intake (mg), 𝑥, and the number of hours spent studying, 𝑦. A scatterplot of the data showed a linear relationship with a slope of 0.164. Interpret the slope.

Answer 9

For every mg of caffeine, the
predicted number of study hours
increases by 0.164 hrs.

Question 10

Desiree randomly selects 20 students at her school and records their caffeine intake (mg), 𝑥, and the number of hours spent studying, 𝑦. A scatterplot of the data showed a linear relationship with a y int. of 2.544 hrs. Interpret the y intercept.

Answer 10

When a student does not have any
caffeine, the predicted number of
hours spent studying is 2.544 hrs.

Question 11

Desiree randomly selects 20 students at her school and records their caffeine intake (mg), 𝑥, and the number of hours spent studying, 𝑦. A scatterplot of the data showed a linear relationship with an R-squared value of 60.032. Interpret R -squared, the coefficient of determination.

Answer 11

About 60.032% of the variation in
study hours is explained by the
linear relationship with caffeine.

Question 12

Desiree randomly selects 20 students at her school and records their caffeine intake (mg), 𝑥, and the number of hours spent studying, 𝑦. A scatterplot of the data showed a linear relationship with an r-squared value of 60.032. Find and interpret r, the correlation coefficient.

Answer 12

𝑟 is 0.7767, indicating that the linear relationship between study hours and caffeine intake is fairly strong and positive.

Note: r and/or an equation of a line
of best fit does not tell you if a linear
model is appropriate. You must see
the original scatterplot and or
residual plot.

Question 13

State 3 ways to decide if a data set is linear.

Answer 13

1. Residual plot does not show a pattern
2. The scatter plot looks linear.
3. r is close to 1 or -1 (or r-squared is close to 1)

Question 14

Desiree randomly selects 20 students at her school and records their caffeine intake (mg), 𝑥, and the number of hours spent studying, 𝑦. A scatterplot of the data showed a linear relationship. The residual for a student whose caffeine in take was 80 mg is −2.72. Interpret the residual.

Answer 14

The actual number of study hours is
2.72 hours below the predicted
value for a student whose caffeine
intake is 80 mg

Question 15

Desiree randomly selects 20 students at her school and records their caffeine intake (mg), 𝑥, and the number of hours spent studying, 𝑦. A scatterplot of the data showed a linear relationship with s = 1.532. Interpret s.

Answer 15

The actual hours spent studying is
typically about 1.532 hours away
from the number predicted by the
LSRL.

Question 16

Desiree randomly selects 20 students at her school and records their caffeine intake (mg), 𝑥, and the number of hours spent studying, 𝑦. Her residual plot shows a random scatter. Interpret the residual plot in the context of the problem.

Answer 16

Since the residual plot shows
random scatter (no clear pattern),
the LSRL relating study hours to
caffeine intake is a linear model.

Question 17

It is certainly plausible that workers are less
likely to quit their jobs when wages are high than when they are low. Let 𝑥 = average hourly wage and 𝑦 = quit rate (number of employees per 100 who left jobs during 1996). The scatterplot of the data has a linear form with a slope of -0.3466. Interpret slope in the context of the problem.

Answer 17

For every additional dollar earned
hourly, the quit rate in 1996 is
predicted to decrease by 0.3466
employees.

Question 18

It is certainly plausible that workers are less
likely to quit their jobs when wages are high than
when they are low. Let 𝑥 = average hourly wage
and 𝑦 = quit rate (number of employees per 100
who left jobs during 1996). The scatterplot of
the data has a linear form with an r squared value of 72.9. Interpret R squared in the context of the problem.

Answer 18

About 72.9% of the variability in quit
rate in 1996 is explained by the linear relationship in hourly wage.

Question 19

It is certainly plausible that workers are less
likely to quit their jobs when wages are high than
when they are low. Let 𝑥 = average hourly wage
and 𝑦 = quit rate (number of employees per 100
who left jobs during 1996). The scatterplot of
the data has a linear form with a s value of 0.4862. Interpret s.

Answer 19

The actual quit rate in 1996 is
typically about 0.4862 employees
from the number predicted by the
LSRL.

Question 20

It is certainly plausible that workers are less
likely to quit their jobs when wages are high than
when they are low. Let 𝑥 = average hourly wage
and 𝑦 = quit rate (number of employees per 100
who left jobs during 1996). The scatterplot of
the data has a linear form with a correlation coefficient of -0.8538. Interpret the correlation coefficient.

Answer 20

𝑟 is −0.8538 indicating that the linear relationship between quit rate in 1996 and hourly wage. is strong and negative

Question 21

It is certainly plausible that workers are less
likely to quit their jobs when wages are high than
when they are low. Let 𝑥 = average hourly wage
and 𝑦 = quit rate (number of employees per 100
who left jobs during 1996). The residual for an hourly wage of $12 is 0.01.Interpret this residual in the context of the problem.

Answer 21

The actual quit rate in 1996 was
0.01 employees above the predicted
value for an hourly wage of $12.

Question 22

It is certainly plausible that workers are less
likely to quit their jobs when wages are high than
when they are low. Let 𝑥 = average hourly wage
and 𝑦 = quit rate (number of employees per 100
who left jobs during 1996). The actual quit rate in 1996 was 0.024 employees below the
predicted value for an hourly wage
of $9. Interpret the residual.

Answer 22

The actual quit rate in 1996 was
0.024 employees below the
predicted value for an hourly wage
of $9.

Question 23

How could you linearize an exponential model?

Answer 23

Graph the log(y values) vs. the x values.

Question 24

How could you linearize a power model?

Answer 24

Graph the log(y values) vs. the log (x values).