Interpret Linear Data in Context

The points in the scatterplot represent paired observations (x, y) where x is an individual’s weight and y is the time (in seconds) it takes for walking on a treadmill to raise the individual’s pulse rate to 140 beats per minute.  The open circles correspond to females and the dark squares to males.

• There is a positive correlation r between gender and weight, since men tend to weigh more than women.

• There is a negative correlation r between weight and time for both males and females.

• In general, males tend to take less time to have their pulse rate raised to 140 bpm while walking on the treadmill.

The scatter plot below shows the number of books read by students in Mrs. Hall’s English class and their final grades. Which statement represents the best description about the line of best fit?

• The more books students read, the lower their English grade.

• The more books students read, the higher their English grade.

• The fewer books students read, the higher their English grade. 

• No relationship exists between the number of books students read and their English grades. 

Some data were collected on the weight of a male while 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. 

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. 

What is the meaning of the slope?

• The cost to get into the fair is $5

• The total cost for the day will increase by $1.75 for every ride you go on.

• The cost to get into the fair is $1.75

• The total cost for the day will increase by $5 for every ride you go on. 

• 4

• 10.75

• 11.75

• 12.75

What does the slope represent?

• 1 movie per millions

• admit one

• salary per movie

• highest paid salary

What does the slope mean in the context of the problem?

• The cost will increase by $1.40 per topping

• The cost will decrease by $1.40 per topping

• The cost will increase by $1.90 per topping

• The cost will decrease by $1.90 per topping 

The table represents a used car salesman's monthly salary including commission made on the sale of cars.  What is the slope and what does it represent?

• The slope is $850/car and it represents the commission per car sold.

• The slope is $425/car and it represents the commission per car sold.

• The slope is $1500 and it represents the monthly salary before commission.

• The slope is $850 and it represents the monthly salary before commission.

Explain what the slope means in context.

• For every 1 minute the total charges decrease by 25 cents.

• For every 1 minute the total charges increase by 25 cents.

• For every 1 minute the total charges decrease by $2.50

• For every 1 minute the total charges increase by $2.50

Answer explanation

The y values increase by $2.50 and the x-values increase by 10.

2.50 divided by 10 is 0.25 (so 25 cents).