Lesson 3 Getting Schooled Solidify Understanding

Ready

The graph several points and the line . Use the graph to answer each problem.

A graph of the y=x line and 8 plotted points B (1, 4), E (2, 5), D (3, 3), G (6, 6), I (6, 5), L (8, 7), N (9, 6), X ( 11, 9) x–1–1–1111222333444555666777888999101010111111y–1–1–1111222333444555666777888999101010111111

1.

The vertical distance between point and the line on the graph is . Find all of the vertical distances between the points and the line .

2.

Calculate the sum of all the distances you found in problem 1.

3.

What is the average of the vertical distances of the points from the line ?

4.

Use technology to calculate the correlation coefficient, and find the equation of the regression line.

Correlation Coefficient:

Regression Line Equation:

5.

How does the line compare to the regression line? Why is this the case?

Set

Find the correlation coefficient and the equation for the line of regression for each table.

6.

Day of Month

Balance in Bank Account

7.

Time (weeks)

Depth of Water in Reservoir (ft)

8.

What is the slope for the table in problem 6?

9.

What does the slope for problem 6 mean in terms of the data set?

10.

Explain the meaning of the equation for problem 7. What do the slope and the -intercept mean for that data set?

11.

The data in problem 6 seems to have a strong, negative correlation. Can we say that the day of the month causes a certain bank balance to occur? Explain.

12.

The data in problem 7 seems to have a strong correlation. Can we say that the number of weeks passed will cause the depth of water to be at a given depth? Explain.

13.

Which graph shows the best model for the data and will create the best prediction? Explain why your choice is the best model for the data.

A.
Graph A shows a curve moving up to the right modeling the data. About 16 of the points beginning at the origin follow the curve while sitting just above it. xy
B.
Graph B shows a curve moving up to the right modeling the data. All of the points are touching the curve. Some are touching from above the curve, some are exactly on the curve, and some are touching from below the curve. xy
C.
Graph C shows a line moving up to the right to model the data. At the beginning of the line 5 points are very close but above the line. Most of the points are below the line but are very close or are touching the line. The last 3 point are above and moving up to the right away from the line. xy

14.

Which graph below shows the best model for the data and will create the best prediction? Explain why your choice is the best model for the data.

A.
Graph A shows a descending curve modeling the data. Three of the points are exactly on the curve. One point sits just above it. The remaining 4 points are below the curve but follow it closely. xy
B.
Graph B shows a descending curve modeling the data. The first point on the left is a full unit above the curve. The next 3 points follow the curve from below the curve and not touching it. The next 2 points are exactly on the curve and the next 1 is touching it from above. The last point is above the curve and not touching it. xy
C.
Graph C shows a descending line to model the data. Beginning from the left, one point is about 2 units above the line. The next point is close to the line but still above it. The next 5 points are below the line, not touching the line, but trending down like the line. The last point is on the line. xy

15.

Is a linear model always the best model for a data set? What type of model appears to be the best for problems 13 and 14?

Go

Classify each of the functions as linear, exponential, or neither of these. Provide justification for the classification.

16.

A.

linear

B.

exponential

C.

neither

17.

A.

linear

B.

exponential

C.

neither

18.

A.

linear

B.

exponential

C.

neither

19.

A.

linear

B.

exponential

C.

neither

20.

A.

linear

B.

exponential

C.

neither

21.

The amount of medicine in the bloodstream of a cat decreases as time passes. The initial dose of medicine is , and the medicine breaks down at each hour.

A.

linear

B.

exponential

C.

neither

22.

Time

Money in Bank

A.

linear

B.

exponential

C.

neither