Linear Correlation & Regression
Name _______________________________
Chapter 4 Homework
Read each problem carefully. Write your answer in the blank, or circle the correct answer.
1. Consider the following scatter diagram.
Do the two variables have a linear relationship?
a) Yes
b) No
Do the two variables have a positive or negative association?
a) Positive
b) Negative
c) Not enough information
2. Use the following data set for the following questions.
X
y
2
8
6
2
6
6
7
9
9
5
Which of the following is the correct scatter diagram of the data?
a)
b)
c)
Calculate the linear correlation coefficient, r. Round to 3 decimals.
r = ___________________
Is there a linear relationship between x and y?
a)
b)
c)
d)
Yes there is a linear relationship because |r| > CV.
No, there is not a linear relationship because |r| > CV.
Yes, there is a linear relationship because |r| < CV.
No, there is not a linear relationship because |r| < CV.
d)
3. A student at a junior college conducted a survey of 20 randomly selected full-time students to
determine the relation between the number of hours of video game playing each week, x, and grade
point average (GPA), y. She found that a linear relation exists between the two variables. The
regression line that describes this relation is: yˆ  0.0558 x  2.9112
Interpret the slope of the regression line:
For each additional hour that a student spends playing video games in a week, the
GPA will _________________ by ____________ points, on average.
(decrease/increase)
Interpret the y-intercept of the regression line (if appropriate):
a) The average number of video games play in a week by students is 2.9112.
b) The GPA of a student who does not play video games is 2.9112
c) It cannot be interpreted.
Predict the GPA of a student who plays video games 8 hours per week. Round to 2 decimals.
GPA = ________________
4. The following data represent the number of days absent, x, and the final grade, y, for a sample of
college students in a general education course at a large state university.
X
Y
0
89
1
86
3
81
4
74
6
84
7
79
Calculate the linear correlation coefficient, r. Round to 3 decimals.
r = ___________________
Is there a linear relationship between absences and final grade?
a) Yes there is a linear relationship because |r| > CV.
b) No, there is not a linear relationship because |r| > CV.
c) Yes, there is a linear relationship because |r| < CV.
d) No, there is not a linear relationship because |r| < CV.
Calculate the regression line for absences vs. final grade.
yˆ  ________ x  _________
Calculate the average final grade, y . Round to the nearest whole number.
y = _________________
Predict the final grade for a student who misses 5 class periods.
Grade = ______________
8
65
5. A pediatrician wants to determine the relation that exists between a child’s height, x and head
circumference, y. She randomly selects 11 children from her practice, measures their heights and
head circumferences and obtains the following data:
x
y
27.75 17.7
Calculate the regression line for height vs. head circumference.
24.5
17.2
Round values to 3 decimals.
25.5
17.1
25.5
17.1
yˆ  _____________ x  ______________
25
16.9
27.75 17.6
27
17.3
Interpret the slope of the regression line:
27
17.5
26.75 17.3
If height increases by 1 inch, head circumference will
26.75 17.5
________________ by about __________ inches, on average.
27.5
17.5
(decrease/increase)
Interpret the y-intercept, if appropriate:
a) The y-intercept is the child’s head circumference when the child’s height is 0 inches.
b) It is not appropriate to interpret the y-intercept because it is outside the scope of the model.
Calculate the linear correlation coefficient, r. Round to 3 decimals.
r = ___________________
Is there a linear relationship between height and head circumference?
a)
b)
c)
d)
Yes there is a linear relationship because |r| > CV.
No, there is not a linear relationship because |r| > CV.
Yes, there is a linear relationship because |r| < CV.
No, there is not a linear relationship because |r| < CV.
Predict the head circumference of a child who is 25 inches tall.
Head Circumference = _____________________ (1 decimal)
Suppose that the actual head circumference of the 25-inch-tall child is 16.9 inches (in the table).
Calculate the residual. Is the head circumference above or below average?
Residual = _____________ inches
Above Average or Below Average
(circle one)
Would it be reasonable to use the regression line to predict the head circumference of a child who was
32 inches tall?
a) Yes, because 32 is within the scope of the data.
b) No, because 32 is not within the scope of the data.