L3-5 and 3-6 Review

Last updated over 2 years ago

20 questions

1

Library

L3-5 and 3-6 Review

Last updated over 2 years ago

20 questions

1

Draggable item		Corresponding Item

1

What type of correlation is demonstrated by the data in the table below?

1

Hana models her spending in the scenario above with the function f(x)=5.5x+11.

A) Use her equation to predict how much she will spend if she buys 8 books.
B) If Hana's original data include purchases of anywhere from 1 to 4 books, is your answer to (A) an example of "extrapolation" or "interpolation"?

1

Given the following results from a linear regression on a data set, provide the equation of the line of best fit for the data. Round all constants and coefficients to the nearest tenth.

1

When a scientist is concerned with the strength of a correlation but not the direction, she may refer to the "r squared" value, r^{2}, which is simply the square of the correlation coefficient, r. Does this make sense? How helpful or harmful is it? Explain your reasoning.

1

Draggable item		Corresponding Item

What type of association is shown by the data in the scatter plot?

positive association

negative association

no association

trend association

What type of association is shown by the data in the scatter plot?

positive association

negative association

no association

trend association

What type of association is shown by the data in the scatter plot?

positive association

negative association

no association

trend association

What type of association is shown by the data in the scatter plot?

positive association

negative association

no association

trend association

What type of association is shown by the data in the scatter plot?

positive association

negative association

no association

trend association

Select all and only the statements that are true of positive associations.

As the x value increases, the y value tends to increase.

As the y value decreases, the x value tends to decrease.

You cannot extrapolate from a positive association.

You can only interpolate in the context of a positive association.

Match each definition with the appropriate vocabulary term.

Draggable item		Corresponding Item
Using a trend line to predict (or "theorize") the y-value for an x-value outside the bounds of the actual data.		positive association
Using a trend line to predict (or "theorize") the y-value for an x-value that is between the x-values of two actual data points.		negative association
a value r, ranging from -1 to 1, which provides a measure of the direction and strength of a correlation.		extrapolation
As the x value increases, the y value tends to increase.		interpolation
As the x value increases, the y value tends to decrease.		correlation coefficient

Which equation best models the data shown in the following scatter plot?

y=x-5

y=3x-3

y=x-3

y=3x-5

What type of correlation is demonstrated by the data in the table below?

Which of the following trend lines best fits the underlying scatter plot data?

When Hana goes to the mall, she always buys the same lunch and also buys some books. The total amount of money she spends, y, is a function of the number of books she buys, x. Which of the following statements are true about this function?

The y-intercept is the cost of Hana's lunch.

The slope is the cost of one book.

The y-intercept is the cost of one book.

The slope is the cost of Hana's lunch.

Hana models her spending in the scenario above with the function f(x)=5.5x+11.

A) Use her equation to predict how much she will spend if she buys 8 books.
B) If Hana's original data include purchases of anywhere from 1 to 4 books, is your answer to (A) an example of "extrapolation" or "interpolation"?

If a linear regression reveals an r value of -0.62376, what can be said about the correlation?

Given the following results from a linear regression on a data set, provide the equation of the line of best fit for the data. Round all constants and coefficients to the nearest tenth.

Choose the best explanation for the model described by the residual plot.

The model is a good fit for the data because the residuals are randomly distributed above and below the x-axis

The model is a bad fit for the data because the residuals demonstrate a clear trend.

The model is a bad fit for the data because the residuals are too big.

The model is a good fit for the data because the residuals are clustered around 1.

Emmy measures the temperature of some hot water left out in the open at various times while the water cools. She then uses a trend line to theorize what the water's temperature was at the moment between two of her measurements. This is an example of:

extrapolation

interpolation

prediction

best fit

Ricardo calculates a line of best fit for a data set with integer x-values 1 through 6. Using a line of best fit with the equation y = –3x + 21 to predict the value of y when x = 10 is an example of:

extrapolation

prediction

interpolation

best fit

Below is sample data relating the hour at which Mr. Schneider wakes up with the amount of coffee (in fl oz) he drinks throughout the day. Is there a correlation if you model his data with a linear equation? Is there a causal relationship?

There is a positive correlation and a causal relationship.

There is a negative correlation and no causal relationship.

There is a negative correlation and a causal relationship.

There is a positive correlation and no causal relationship.

When a scientist is concerned with the strength of a correlation but not the direction, she may refer to the "r squared" value, r^{2}, which is simply the square of the correlation coefficient, r. Does this make sense? How helpful or harmful is it? Explain your reasoning.

Vocabulary Bonanza! Match each noun phrase with its correct counterpart.

Draggable item		Corresponding Item
domain		a pair of values associated with a single unit of observation
A point on a line		a visual representation of the solution set of the equation
A line of best fit		An ordered pair of values (x, y) such that those values make the linear equation a true statement.
correlation coefficient		The linear equation which results from a regression (e.g., one that minimizes the sum of the squared residuals)
translation		a number -1\leq r\leq 1 that measures the strength and direction of a correlation
range		a transformation of a function in which every point moves the same distance in the same direction
The graph of a linear equation		the set of all possible inputs of a function
A point on a scatter plot		the set of all outputs of a function

What type of association is shown by the data in the scatter plot?

positive association

negative association

no association

trend association

What type of association is shown by the data in the scatter plot?

positive association

negative association

no association

trend association

What type of association is shown by the data in the scatter plot?

positive association

negative association

no association

trend association

What type of association is shown by the data in the scatter plot?

positive association

negative association

no association

trend association

What type of association is shown by the data in the scatter plot?

positive association

negative association

no association

trend association

Select all and only the statements that are true of positive associations.

As the x value increases, the y value tends to increase.

As the y value decreases, the x value tends to decrease.

You cannot extrapolate from a positive association.

You can only interpolate in the context of a positive association.

Match each definition with the appropriate vocabulary term.

Using a trend line to predict (or "theorize") the y-value for an x-value outside the bounds of the actual data.

positive association

Using a trend line to predict (or "theorize") the y-value for an x-value that is between the x-values of two actual data points.

negative association

a value r, ranging from -1 to 1, which provides a measure of the direction and strength of a correlation.

extrapolation

As the x value increases, the y value tends to increase.

interpolation

As the x value increases, the y value tends to decrease.

correlation coefficient

Which equation best models the data shown in the following scatter plot?

y=x-5

y=3x-3

y=x-3

y=3x-5

Which of the following trend lines best fits the underlying scatter plot data?

When Hana goes to the mall, she always buys the same lunch and also buys some books. The total amount of money she spends, y, is a function of the number of books she buys, x. Which of the following statements are true about this function?

The y-intercept is the cost of Hana's lunch.

The slope is the cost of one book.

The y-intercept is the cost of one book.

The slope is the cost of Hana's lunch.

If a linear regression reveals an r value of -0.62376, what can be said about the correlation?

It is strongly positive

It is weakly positive

It is strongly negative

It is weakly negative

There is no correlation, or very weak correlation.

Choose the best explanation for the model described by the residual plot.

The model is a good fit for the data because the residuals are randomly distributed above and below the x-axis

The model is a bad fit for the data because the residuals demonstrate a clear trend.

The model is a bad fit for the data because the residuals are too big.

The model is a good fit for the data because the residuals are clustered around 1.

Emmy measures the temperature of some hot water left out in the open at various times while the water cools. She then uses a trend line to theorize what the water's temperature was at the moment between two of her measurements. This is an example of:

extrapolation

interpolation

prediction

best fit

Ricardo calculates a line of best fit for a data set with integer x-values 1 through 6.  Using a line of best fit with the equation y = –3x + 21 to predict the value of y when x = 10 is an example of:

extrapolation

prediction

interpolation

best fit

Below is sample data relating the hour at which Mr. Schneider wakes up with the amount of coffee (in fl oz) he drinks throughout the day. Is there a correlation if you model his data with a linear equation? Is there a causal relationship?

There is a positive correlation and a causal relationship.

There is a negative correlation and no causal relationship.

There is a negative correlation and a causal relationship.

There is a positive correlation and no causal relationship.

Vocabulary Bonanza! Match each noun phrase with its correct counterpart.

domain

a pair of values associated with a single unit of observation

A point on a line

a visual representation of the solution set of the equation

A line of best fit

An ordered pair of values (x, y) such that those values make the linear equation a true statement.

correlation coefficient

The linear equation which results from a regression (e.g., one that minimizes the sum of the squared residuals)

translation

a number -1\leq r\leq 1 that measures the strength and direction of a correlation

range

a transformation of a function in which every point moves the same distance in the same direction

The graph of a linear equation

the set of all possible inputs of a function

A point on a scatter plot

the set of all outputs of a function