Linear Interpretation and Scatterplot

A scatterplot shows a strong, positive, linear relationship between the number of rebounds a basketball team averages and the number of wins that team records in a season. Which conclusion is most appropriate?

• A team that increases its number of rebounds causes its chances of winning more games to increase.

• If the residual plot shows no pattern, then it is safe to conclude that getting more rebounds causes more wins, on average.

• If the residual plot shows no pattern, then it is safe to conclude that getting more wins causes more rebounds, on average.

• If the r^2 value is close enough to 100%, then it is safe to conclude that getting more rebounds causes more wins, on average.

• Rebounds and wins are positively correlated, but we cannot conclude that getting more rebounds causes more wins, on average.

Data are collected on the amount of fat (in grams) and calories in the french fry orders at nine fast food restaurants. The least-squares regression line for the data is y = 274.34 + 9.55x, where y is the predicted number of calories and x is grams of fat. Which of the following is the correct interpretation of the slope of the least-squares regression line?

• The calories increase by 9.55, on average.

• For every increase in fat, the calories increase as well.

• Every increase of 1 gram of fat causes an increase of 9.55 calories.

• For every increase of 1 gram of fat, the predicted calories increase by 9.55.

• For every increase of 1 calorie, the predicted grams of fat increase by 9.55.

The scatterplot shows data for nine french fry orders. A tenth fast food chain has been added, as indicated by the arrow. How would this tenth data point affect the slope and correlation in this scenario?

• Slope decreases, correlation increases

• Slope increases, correlation increases

• Slope increases, correlation decreases

• Slope decreases, correlation decreases

• Cannot be determined without the full set of data

A random sample of households is taken. For each household, the number of hours spent watching television and the power consumption (in kWh) during a day are recorded. The table below shows computer output from a linear regression analysis on the data. Which of the following is the equation of the least-squares regression line?

• ŷ = 19.31 + 0.891x

• ŷ = 2.8621 + 0.2715x

• ŷ = 0.891 + 19.31x

• ŷ = 0.2715 + 2.8621x

• ŷ = 0.2715 + 0.891x

A random sample of households is taken. For each household, the number of hours spent watching television and the power consumption (in kWh) during a day are recorded. The table below shows computer output from a linear regression analysis on the data. Which of the following is a correct interpretation of r²?

• Number of hours of television explains 30% of the variability in power consumption.

• 30% of the increase in number of hours of television is explained by power consumption.

• 30% of the data will lie on the least-squares regression line.

• 30% of the residuals will be less than 4.185.

• All of the above are correct interpretations.

In a scatterplot r is called

• Coefficient of Determination

• Correlation coefficient

• Regression Line

• Slope

Which of the following relationships between two variables could be described using correlation, r?

• Number of books read and gender of a student.

• Number of football games played and the position of a football player.

• High temperature of the day and number of zoo visitors that day.

• Type of beverage ordered and time of day it was ordered.

• Brand of cell phone and number of cell phones sold.

Shown is a residual plot. Would a linear regression model of the data be most appropriate?

• YES

• NO

Would the linear model be appropriate?

• YES

• NO

Can you predict the battery life of a tablet using the price? Using the data from a sample of 15 tablets, the LSRL y-hat=4.67 + 0.0068x was calculated using x=price in dollars and y= battery life in hours. S=1.21 and r²=0.342. Which is the correct interpretation of the coefficient of determination.

• 34.2% of the variability in battery life is explained by the LSRL with x=price in dollars.

• The actual battery life in hours is typically 1.21 hours away from the battery life predicted by the LSRL

• There is a weak positive linear association between price in dollars and battery life.

• We predict the battery life of a tablet will increase 0.0068 hours for each increase of $1 in price