Lesson 3 Getting Schooled Solidify Understanding

Ready

The graph shows several points and the line $y = x$ . Use the graph to answer each problem.

1.

The vertical distance between point $N$ and the line $y = x$ on the graph is $3$ . Find all of the vertical distances between the points and the line $y = x$ .

$B :$

$D :$

$E :$

$G :$

$I :$

$L :$

$N :$

$X :$

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 $y = x$ ?

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 $y = x$ 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 $($)$
$5$	$1,576$
$12$	$1,324$
$18$	$1,192$
$23$	$973$
$28$	$808$
$30$	$679$

7.

Time (weeks)	Depth of Water in Reservoir (ft)
$1$	$615$
$3$	$613.5$
$5$	$611$
$8$	$610.8$
$12$	$608$
$16$	$605.4$
$22$	$601.6$

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 $y$ -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.

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.

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.

$x$	$y$
$0$	$12$
$1$	$12$
$2$	$12$
$3$	$12$
$4$	$12$

linear

exponential

neither

17.

$x$	$y$
$1$	$15$
$2$	$20$
$3$	$27$
$4$	$36$
$5$	$47$

linear

exponential

quadratic

none of these

18.

$x$	$y$
$- 6$	$- 2$
$- 5$	$- 3$
$- 4$	$- 4$
$- 3$	$- 5$
$- 2$	$- 6$

linear

exponential

neither

19.

$y = {(x + 8)}^{2} - 13$

linear

exponential

quadratic

none of these

20.

$y = 3 \cdot 4^{(x - 1)}$

linear

exponential

neither

21.

The amount of medicine in the bloodstream of a cat decreases as time passes. The initial dose of medicine is $80 mg$ , and the medicine breaks down at $35 %$ each hour.

linear

exponential

neither

22.

Time	$0$	$1$	$2$	$3$	$4$
Money in Bank	$$ 250$	$$ 337.50$	$$ 455.63$	$$ 615.09$	$$ 830.38$

linear

exponential

neither