3.2.2 - Interpreting Slope & Y-Intercept

Which of the following statements about the slope of the least-squares regression line is true? 

• It has the same sign as the correlation coefficient r.
• The square of the slope equals the proportion of the variation in the response variable that is explained by the explanatory variable.
• It is unitless.
• When the x-variable is 0, this is what the y-variable is predicted to be.

Tags

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.7

Some data were collected on the weight of a male white laboratory rat for the first 25 weeks after its birth. The linear regression equation is:
Weight = 100 + 40(Time).
Which is the best description of the slope for this regression equation in context of the problem?

• The slope of the line of regression is the time since birth of the rate. It demonstrates the predicted weight of a laboratory rate after so many months since birth.
• The slope is 40 grams/week which means the mouse gains about 40 grams per week after birth.
• The slope is 40 and it means for every increase in weeks the graph will increase. 
• The slope is 40, which tells us the line increases. 

Tags

CCSS.HSF.LE.B.5

Which is the best description of the y - intercept for the linear regression equation of the rats: Weight = 100 + 40(Time)?

• The y-intercept is 100, which means the rat is predicted to weigh 100 grams at birth. 
• The y-intercept is 100, which is where the graph crosses the y-axis. 
• 100 is where the data starts on the y-axis. 
• The y-intercept is 100, which means at a weight of 0, the rat will take 100 seconds.

Tags

CCSS.HSF.LE.B.5

For the years 1950-1980, the number of heart disease deaths per 100,000 people in the United States were recorded. The regression line below was computed using a statistical software package. which statement is the correct interpretation of the slope?

The regression equation is

Number of deaths = 7387 - 3.63 year

• Heart disease will be cured in the year 2036.

• The regression line estimates that for every 3.63 years there is an average of 1 death due to heart disease per 100,000 people.

• For every 3.63 years there is a decrease on the average of 1 death due to heart disease per 100,000 people.

• There is an increase of approximately 7387 deaths per year.

• The number of heart disease deaths per 100,000 people has been dropping by an estimated 3.63 deaths per year on the average.

Tags

CCSS.8.SP.A.3

Data on x = the weight of a pickup truck (pounds) and y = distance (in feet) required for a truck traveling 40 miles per hour to come to a complete stop for 30 trucks was used to fit the least squares regression line y^hat = 26 + 0.05x. Which of the following statements is a correct interpretation of the value 26 in the equation of the regression line?

• On average, the stopping distance increases by 26 feet for each 1-pound increase in truck weight.

• On average, the truck weight increases by 26 pounds for each additional foot in stopping distance.

• Approximately 26% of the variation in the stopping distances can be explained by the linear relationship between stopping distance and truck weight.

• It is not reasonable to interpret the intercept in this setting because a weight of 0 is outside the range of the data used to fit the regression line.

Tags

CCSS.8.SP.A.3

The equation y = -2x + 7 models the amount of gas 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.

Tags

CCSS.HSF.LE.B.5

The relation between the selling price of a car (in $1,000) and its age (in years) is estimated from a random sample of cars of a specific model. The relation is given by the following formula:

SellingPrice = 24.2 − (1.182)Age

Which of the following can be concluded from this equation?

• For every year the car gets older, the selling price drops by approximately $2420.

• For every year the car gets older, the selling price goes down by approximately 11.82 percent.

• On average, a new car costs about $11,820.

• On average, a new car costs about $23,018.

• For every year the car gets older, the selling price drops by approximately $1182.

Above is a table that represents the distance in miles vs. the cost of a plane ticket. What does the slope mean in the regression equation  $y=0.136x+74$  

• A plane ride costs $0.136 (13 cents)

• For every 1 mile flown, the cost goes up  $ 0.136 dollars (13 cents)

• For every 1 mile flown, the cost goes up $74

Tags

CCSS.HSF.LE.B.5

The equation  $y\sim1.40t\ +1.90$   represents the cost of a hamburger with t  toppings. What does the y-intercept mean in this context?

• A hamburger with 0 toppings costs $1.90

• Every hamburger costs $1.90

• A hamburger with 1.40 toppings costs $1.90

• Every topping adds $1.40 to the cost of the hamburger

Tags

CCSS.HSF.LE.B.5

predicted math grade = 65 + 2.56(study hours)

What does the slope mean in context?

• The model predicts an increase of 2.56 points in the math grade per hour studied, on average.

• The model predicts an increase of 65 points in the math grade per hour studied, on average.

• The model predicts an increase of 2.56 study hours per math grade, on average.

• The model predicts an increase of 2.56 study hours, on average.

Tags

CCSS.HSF.LE.B.5