The vertical distance between a data point and the line of best fit

The difference between the actual value and the predicted value

An error when looking at data representing an entire population

A substance that remains after a process of changing states of matter

What is the process of figuring out which line is the BEST fit by finding the line that minimizes the sum of least square residuals?

Ordinary Least Squares (OLS) Regression

Since the line of best fit always has residuals that sum to 0, then squaring the distances gives more information. The outliers will weigh more heavily because the squared value is very large for points that are farther from the line. The equation for this regression line is y = -0.16x + 18 . Which of the following statements about the slope is correct?

The slope is -0.16 . This means the predicted student:faculty ratio decreases by 0.16 for every additional $1000 in tuition .

The slope is -0.16 . This means the predicted student:faculty ratio is the tuition multiplied by 0.16.

The slope is 18 . This means the predicted student:faculty ratio increases by 18 for every additional $1000 in tuition.

The slope is 18 . This means the average student:faculty ratio is 18.

The slope cannot be determined.

Which of the following is important to know about r 2 ?

r 2 is a number between 0 and 1

r 2 cannot be used to check if the coefficient estimates and predictions are biased or not

A high r 2 value means the points are close to the line of best fit.

r 2 does not inform whether or not the regression model has an adequate fit

r 2 tells how well the model can predict the data

Ethan concludes, "The slope of the line of best fit is 0.87. That means that if a college increases their sticker price by $1000, it will cause their graduation rate to increase by 0.87 percentage points." Is Ethan correct? Why or why not?

No , Ethan is incorrect. Correlation DOES NOT imply causation.

Yes , Ethan is correct. Correlation WILL ALWAYS imply causation.

Yes , Ethan is correct. The slope of the line is positive.

No , Ethan is incorrect. The correlation is weak.

Kiana is researching how the costs of college have changed over time. She finds data on the average annual cost of attending a 4-year college since 1970, adjusted for inflation. It includes the cost of tuition, required fees, housing, and food. Kiana uses linear regression to find the line of best fit. Her results are shown in the graph. What does the slope tell you in this context?

Positive correlation, cost of college is expected to increase $420 each year

Strong correlation, cost of college is expected to increase $420 each year

Negative correlation, cost of college is expected to decrease $420 each year

Weak correlation, cost of college is expected to increase $0.42 each year

Positive correlation, cost of college is expected to increase $0.42 each year

Kiana is researching how the costs of college have changed over time. She finds data on the average annual cost of attending a 4-year college since 1970, adjusted for inflation. It includes the cost of tuition, required fees, housing, and food. After trying a linear model, Kiana decides to also try an exponential regression model. Her results are shown in the graph. Based on the exponential model, how much are college costs increasing each year?

Based on the exponential model, college costs increase by 2.3% each year

Based on the exponential model, college costs increase by $9900 each year

Based on the exponential model, college costs increase by $9.90 each year

Based on the exponential model, college costs increase by $230 each year

Based on the exponential model, college costs increase by $0.23 each year

A residual plot is a graph that shows just the residuals from a regression model. Analyzing it can help you notice patterns and determine whether you’ve chosen the best type of function to fit the data. For a point above the line of best fit . . .

The residual will be equal to zero

The residual will be equal to the predicted y value

A residual plot is a graph that shows just the residuals from a regression model. Analyzing it can help you notice patterns and determine whether you’ve chosen the best type of function to fit the data. If a data point has a residual of -4, that means . . .

The data point is below the line of best fit

The data point is above the line of best fit

The data point is on the line of best fit

NGPF 9.6 Interpreting Regression Models

Authored by Linda Miragliotta

Mathematics

9th - 12th Grade

CCSS covered

Used 6+ times

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33 questions

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FILL IN THE BLANK QUESTION

15 mins • 3 pts

Harper says, “Let’s add up the total distance we would collectively need to travel to get to each restaurant.”
What is the sum of the distances the friends will travel to Café Mezze?

Harper says, “Let’s add up the total distance we would collectively need to travel to get to each restaurant.”
What is the sum of the distances the friends will travel to Rabat Restaurant?

Harper says, “Let’s add up the total distance we would collectively need to travel to get to each restaurant.”
Why isn’t Harper’s strategy a helpful representation of the scenario?

All 3 friends live the same distances away from each restaurant.

Both totals are 18 miles, so there is no difference between the sums to weigh a decision.

Jaxon has the median distance from Cafe Mezze, but Harper has the median distance from Rabat Restaurant.

Harper is closest to Cafe Mezze and Luke is closest to Rabat Restaurant.

Luke is farthest from Cafe Mezze and Jaxon is farthest from Rabat Restaurant.

FILL IN THE BLANK QUESTION

15 mins • 3 pts

Luke says, “Of course Harper would suggest that, they live right next to Café Mezze! Let’s square the distance each would travel, then find the sum.”
Square the distance each friend would travel to Café Mezze.
What is the sum of those squares?
___miles²

FILL IN THE BLANK QUESTION

15 mins • 3 pts

Luke says, “Of course Harper would suggest that, they live right next to Café Mezze! Let’s square the distance each would travel, then find the sum.”
Square the distance each friend would travel to Rabat Restaurant.
What is the sum of those squares?
___miles²

MULTIPLE CHOICE QUESTION

15 mins • 3 pts

Luke says, “Of course Harper would suggest that, they live right next to Café Mezze! Let’s square the distance each would travel, then find the sum.”
Using Luke’s strategy, why is one of the sums much larger than the other?

Squares are always larger than sums.

Sums are a way to break even.

The Distance Formula finds the most direct route.

Squaring larger numbers gives more weight to greater values than to smaller numbers.

The Pythagorean Theorem calculates larger numbers.

MULTIPLE CHOICE QUESTION

15 mins • 3 pts

Which is the best spot for the friends to meet up?
Which option should the friends choose? Why?

Cafe Mezze because is it closest to Harper and Jaxon.

Rabat Restaurant because it is closest for Luke.

Rabat Restaurant because Harper is being selfish to want to go to the restaurant that they live next to.

Either spot would be equally fair for each of the friends.

Rabat Restaurant because each friend would travel approximately the same distance to get there.

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NGPF 9.6 Interpreting Regression Models

Harper says, “Let’s add up the total distance we would collectively need to travel to get to each restaurant.”
What is the sum of the distances the friends will travel to Café Mezze?

Harper says, “Let’s add up the total distance we would collectively need to travel to get to each restaurant.”
What is the sum of the distances the friends will travel to Rabat Restaurant?

Harper says, “Let’s add up the total distance we would collectively need to travel to get to each restaurant.”
Why isn’t Harper’s strategy a helpful representation of the scenario?

Luke says, “Of course Harper would suggest that, they live right next to Café Mezze! Let’s square the distance each would travel, then find the sum.”
Square the distance each friend would travel to Café Mezze.
What is the sum of those squares?
___miles²

Luke says, “Of course Harper would suggest that, they live right next to Café Mezze! Let’s square the distance each would travel, then find the sum.”
Square the distance each friend would travel to Rabat Restaurant.
What is the sum of those squares?
___miles²

Luke says, “Of course Harper would suggest that, they live right next to Café Mezze! Let’s square the distance each would travel, then find the sum.”
Using Luke’s strategy, why is one of the sums much larger than the other?

Which is the best spot for the friends to meet up?
Which option should the friends choose? Why?

What is a residual?

What is the average student grant aid for the school that admits 10% of students? Estimate based on the data point.

What does Kelly's line of best fit predict the average student grant aid will be for a school that admits 10% of students?
Estimate based on the graph or by using the equation for the line of best fit: ŷ = -0.32x + 45.50. If x = 10, calculate ŷ.

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

NGPF 9.6 Interpreting Regression Models

Harper says, “Let’s add up the total distance we would collectively need to travel to get to each restaurant.” What is the sum of the distances the friends will travel to Café Mezze?

Harper says, “Let’s add up the total distance we would collectively need to travel to get to each restaurant.”What is the sum of the distances the friends will travel to Rabat Restaurant?

Harper says, “Let’s add up the total distance we would collectively need to travel to get to each restaurant.”Why isn’t Harper’s strategy a helpful representation of the scenario?

Luke says, “Of course Harper would suggest that, they live right next to Café Mezze! Let’s square the distance each would travel, then find the sum.” Square the distance each friend would travel to Café Mezze. What is the sum of those squares?___miles2

Luke says, “Of course Harper would suggest that, they live right next to Café Mezze! Let’s square the distance each would travel, then find the sum.” Square the distance each friend would travel to Rabat Restaurant. What is the sum of those squares?___miles2

Luke says, “Of course Harper would suggest that, they live right next to Café Mezze! Let’s square the distance each would travel, then find the sum.” Using Luke’s strategy, why is one of the sums much larger than the other?

Which is the best spot for the friends to meet up?Which option should the friends choose? Why?

What is a residual?

What is the average student grant aid for the school that admits 10% of students? Estimate based on the data point.

What does Kelly's line of best fit predict the average student grant aid will be for a school that admits 10% of students? Estimate based on the graph or by using the equation for the line of best fit: ŷ = -0.32x + 45.50. If x = 10, calculate ŷ.

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Harper says, “Let’s add up the total distance we would collectively need to travel to get to each restaurant.”
What is the sum of the distances the friends will travel to Café Mezze?

Harper says, “Let’s add up the total distance we would collectively need to travel to get to each restaurant.”
What is the sum of the distances the friends will travel to Rabat Restaurant?

Harper says, “Let’s add up the total distance we would collectively need to travel to get to each restaurant.”
Why isn’t Harper’s strategy a helpful representation of the scenario?

Luke says, “Of course Harper would suggest that, they live right next to Café Mezze! Let’s square the distance each would travel, then find the sum.”
Square the distance each friend would travel to Café Mezze.
What is the sum of those squares?
___miles²

Luke says, “Of course Harper would suggest that, they live right next to Café Mezze! Let’s square the distance each would travel, then find the sum.”
Square the distance each friend would travel to Rabat Restaurant.
What is the sum of those squares?
___miles²

Luke says, “Of course Harper would suggest that, they live right next to Café Mezze! Let’s square the distance each would travel, then find the sum.”
Using Luke’s strategy, why is one of the sums much larger than the other?

Which is the best spot for the friends to meet up?
Which option should the friends choose? Why?

What does Kelly's line of best fit predict the average student grant aid will be for a school that admits 10% of students?
Estimate based on the graph or by using the equation for the line of best fit: ŷ = -0.32x + 45.50. If x = 10, calculate ŷ.