Linear Regression
What is the linear regression equation?
y1~mx1+b
True or False
This is an example of causation:
More ice cream sales and more sunburns happen at the same time. They correlate (both go up), but one doesn't cause the other.
False. This is an example of correlation.
correlation = togetherness, not cause.
The linear regression equation for a data set is y = 21.2x + 23.5, where y represents the number of balloons sold by a party store each week and x represents the week number. Use the equation to predict the number of balloons the store will sell during week 8. Round to the nearest whole number.
a. 193
b. 214
c. 236
d. 257
What should be true in order for a scatter plot to show that a linear fit may be appropriate for a data set?
a. The points should form an upward curve.
b. The points should be scattered randomly.
c. The points should appear to lie generally along a line.
d. The points should form one line above the x-axis and another below it.
Answer: C - The points should appear to lie generally along a line.
Shelby’s printer had 500 sheets of paper in it. After Monday, there were 466 sheets of paper. After Tuesday, there were 432 sheets of paper. After Wednesday, there were 398 sheets of paper. If this pattern continues, how many sheets of paper will be left after Friday?
a. 34
b. 296
c. 330
d. 364
C. 330
What type of calculator do you use to find the linear regression equation?
DESMOS
A common saying is “an apple a day keeps the doctor away,” meaning the more fruits and vegetables you eat, the less often you get sick. Is eating fruits and vegetables a necessary condition for not getting sick? Why or why not?
No, a person cannot get sick for reasons not realted to eating fruits and vegetables
******Use these linear regression equations: ****
f(x) = 3.5x + 47
f(x) = 3x + 47
x= hours
If Spencer studied for a total of 16 hours for the next test, what would he expect to earn on the test. Find two answers
Answer: 103% & 95%
TRUE OR FALSE
The correlation coefficient is 0.989 is not a good fit.
FALSE This is a good fit as it is close to 1.
What is the common ratio of the sequence 6, − 3, 1.5, − 0.75 ?
a. − 2
b. − 0.5
c. 0.5
d. 2
B. -0.5
____________________ is the process of using a regression equation to make predictions within the data set.
Hint: vocab word from Lesson 1
Interpolation
A study reveals that drivers who wear seat belts are less likely to experience a severe head injury from an accident. List one confounding variables that could have had an effect on this claim.
Drivers who wear seatbelts might have fewer head injuries from because they are safer in general and take other precautions to avoid accidents.
The accidents that occur to drivers who wear seatbelts may be less severe because they are more experienced drivers and take less risks.
Using this linear regression equation:
y=30x + 12
Predict the distance traveled after 9 miles.
Let x=hours
30(9) + 12 = 282 miles
TRUE OR FALSE
The R value is the coefficient of determination.
FALSE
The r value is the correlation coefficient
Which is a linear function? Hint: slope intercept form
a. f(x) = x + 2
b. f(x) = x2
c. f(x) = 2x
d. f(x) = |2x|
A. f(x) = x + 2
_______________________ is the process of using a regression equation to make predictions beyond the data set.
Hint: Vocabulary word from Lesson 1
Extrapolation
Which statement suggests causation?
a. When you are at the beach, you get wet.
b. When you study for a test, your classmate studies too.
c. When you carry an umbrella to school, it rains.
d. When you don’t brush your teeth, you get cavities.
D. When you don't brush your teeth, you get cavities.
The linear regression equation for a data set is
y = − 2.8x + 70.8, where y is the temperature in degrees Fahrenheit and x is the number of hours since 8 a.m. What does the slope of the equation represent?
a. For each hour that goes by, the temperature decreases 2.8 degrees Fahrenheit.
b. For each hour that goes by, the temperature increases 2.8 degrees Fahrenheit.
c. For each hour that goes by, the temperature decreases 70.8 degrees Fahrenheit.
d. For each hour that goes by, the temperature increases 70.8 degrees Fahrenheit.
Answer: A. For each hour that goes by, the temperature decreases 2.8 degrees Fahrenheit.
The table shows Adam’s age and shoe size. What is the correlation coefficient of the linear regression equation of the line of best fit for the data? Use DESMOS
Age 6 8 10 12
Shoe Size 3 4.5 5 7.5
a. − 1.3
b. 0.7
c. 0.933
d. 0.966
D. 0.966
Which type of function is f(x) = 5x ?
a. Linear absolute value function
b. Exponential function
c. Quadratic function
d. Linear function
B. Exponential function
The table shows the amount Andre earned as a server. The money, in dollars, is the total amount he earned. USE DESMOS
Times (hours) 0 1 2 3 4 5 6 7
Money (dollars) 0 16 35 47 60 69 90 103
Determine a linear regression equation for the data. Round the slope and y-intercept to the nearest whole number.
y = 14x+12
Which statement describes a correlation and a causation? Select all that apply.
a. Drivers who speed have more wrecks.
b. A plant grows more when it is sunny.
c. When Tina leaves for school, her brother does too.
d. Less time spent exercising contributes to weight gain.
3 answers: A, B and D
What is the linear regression equation for the points
(− 2, 2), (0, 1), and (3, 1)? Use Desmos
a. y = 0.18x + 1.4
b. y = 0.18x − 1.4
c. y = − 0.18x + 1.4
d. y = − 0.18x − 1.4
Answer: C. y=-0.18+1.4
What does a correlation coefficient of r = − 0.01 imply about the graph of a data set modeled by a linear regression? Select all that apply. (2 answers)
a. Generally, the slope is positive.
b. Generally, the slope is negative.
c. A linear model is a good fit for the data.
d. A linear model is not a good fit for the data.
B. Generally, the slope is negative
D. A linear model is not a good fit for the data.
Look at question #2 on your review sheet.
1.). What is the linear regression equation
2.) Predict the amount of feed in December. Question 2c on your review.
3.). Predict the amount of feed in February. Question 2d on your review.
4.). True or False. Is the linear regression equation a good indicator until the feed is gone?
1. y = 77.67 + 944.32
2. 245.29
3. 89.95
4. True