3.3 - Linear Regression Review

A restaurant sells pizza for the prices in the data table. Calculate the linear regression equation of the data.

• y = 1.5x + 12

• y = 12x + 1.5

• y = 0.67x - 8

• y = -8x + 0.67

Answer explanation

Calculator steps:

1. Stat --> Edit

2. Enter Toppings in L1, Prince in L2

3. Stat --> Calc

4. Choose #4 - LinReg, enter

y = ax + b

a = 1.5

b = 12

Answer: y = 1.5x + 12

Tags

CCSS.8.EE.C.8C

If Gold's Gym is looking to buy 30 TVs, how much will each one cost?

• 400

• 750

• 1250

• 0

Answer explanation

1. Go to 30 on the x-axis (number of tvs), find 30.

2. Go up to the best prediction on the line at 30.

3. When you trace from that point over to the y-axis, it's a little below 500. Therefore 400 is the best answer.

Tags

CCSS.7.RP.A.2D

The scatter plot shows the relationship between the number of chapters and the total number of pages for several books. Use the trend line to predict how many chapters would be in a book with 180 pages.

• 12 chapters

• 15 chapters

• 18 chapters

• 21 chapters

Answer explanation

1. The y-axis represents number of pages. Find 180 on the y-axis.

2. Trace it over to the line of best fit.

3. The line represents the point (18, 180). 18 chapters are 180 pages.

Tags

CCSS.HSF.BF.A.2

The scatter plot below shows the number of books read by students in Mrs. Hall’s English class and their final grades. Which statement represents the best description about the line of best fit?

• The more books students read, the lower their English grade.

• The more books students read, the higher their English grade.

• The fewer books students read, the higher their English grade.

• No relationship exists between the number of books students read and their English grades.

Answer explanation

This graph has a (slightly) positive correlation. Therefore as x increases, y increases.

Tags

CCSS.8.EE.B.5

Which color best represents the line of best fit?

• A) Black

• B) Orange

• C) Red

• D) Blue

Answer explanation

The Line of Best Fit is the line that goes through the middle of the data.

Tags

CCSS.8.SP.A.2

If x is temperature and y is coffee sales, use the following formula to determine the coffee sales on a 34° day.

y = -60x+6443

• $4403

• $4673

• $8483

• $6443

Answer explanation

Using the prediction equation y = -60x + 6443 where x is temperature used to predict y, coffee sales.

Since 34 degrees represents temperature, plug 34 in for x.

y = -60(34) + 6443

y = 4403

Tags

CCSS.HSF.LE.B.5

The equation y = -2x + 7 models the amount of gas (in gallons) remaining in a lawnmower after x hours of use since it was filled. What is the meaning of the slope?

• For each hour of mowing, the mower is predicted to use 2 gallons.

• the predicted amount of gas the lawnmower can hold is 2 gallons

• For every two hours of mowing, the mower is predicted to use 7 gallons.

• The predicted amount of gas remaining after 1 hour is 2 gallons.

Answer explanation

Slope is rate of change.

Change in y over change in x.

In this scenario x represents hours and y represents amount of gas.

The slope of this line is -2 or -2/1.

The change in y (gas) is -2 gallons. The change in y (hours) is 1.

So the lawnmower uses 2 gallons every hour.

Tags

CCSS.HSF.LE.B.5

Rich is a member of a gym. He pays a monthly fee plus a per-visit fee. The equation below represents the monthly amount Rich pays for his membership to the gym per month for x visits.

y= 10 + 3x

What does the y-intercept of the graph of this equation represent?

• The monthly fee

• How much Rich pays per visit

• The number of times Rich goes to the gym

• The total cost at the end of the month

Answer explanation

The y-intercept is when x=0, or at the start of the story.

In this case, the y-intercept is when x (# of visits) is 0.

The two parts of the equation are a monthly fee + a per-visit fee (dependent on number of visits). That makes the monthly fee the y-intercept. It does not change depending on the number of visits.

Tags

CCSS.HSF.LE.B.5

The table shown is comparing a person's foot length to their height in cm. Calculate a line of best fit.

• f(x) = 25.05x + 5.57

• f(x) = 5.57x + 25.05

• f(x) = -5.57x + 25.05

• f(x) = 5.57x - 25.05

Answer explanation

1. Stat, Edit

2. Enter x-values in L1 and y-values in L2

3. Stat, Calc

4. Choose #4 - LinReg, Enter

y = ax + b

a = 5.57073955

b = 25.05144695

y = 5.57x + 25.05

Tags

CCSS.HSA.CED.A.2

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.7

The table shows the height of a tree for various years after it was planted. Using the line of best fit, how tall would the tree be 30 years after it was planted?

• 22 feet

• 23 feet

• 36 feet

• 37 feet

Answer explanation

1. Stat, Calc

2. Enter Age into L1, Height into L2

3. Stat, Calc, Enter

y = ax + b

a = 0.964444

b = 8.471111

y = 0.96x + 8.47

4. Thirty represents years, or x. Plug 30 in for x

y = 0.96(30) + 8.47

y = 37.27

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6