Slope and Y-Interpretation in a Scatterplot

Use the scatterplot and computer printout shown above to answer the following question. Write the equation of the least squares regression line.

• ŷ = -.050 + 0.07x

• ŷ = -0.50 - 0.866x

• ŷ = 8.66 - 0.50x

• ŷ = 8.66 + 0.69x

• ŷ = 12.55 - 6.81x

If the data point in the lower right-hand corner of the graph is removed, which of these will be the result?

• The slope of the least squares regression line will decrease and the correlation will increase.

• The slope of the least squares regression line will increase and the correlation will increase.

• The slope of the least squares regression line will decrease and the correlation will decrease.

• The slope of the least squares regression line will increase and the correlation will decrease.

• The slope of the least squares regression line and the correlation will remain the same.

A scatterplot shows a linear association, and a residual plot for the linear regression shows no pattern. The regression yielded the information shown above. Which of the following is false?

• The LSRL is a good linear model for this data.

• The high R value means that it is reasonable to assume a cause-and-effect relationship between the two variables.

• Because a new LSRL after removal of one of the points is

  ŷ = 16.72 + 2.51x, the point that was removed can be considered an influential point.

• For every unit increase in x, the predicted y-value will increase by approximately 2.701 units.

• The association is strong and positive.

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.

• A
• B
• C
• D

The graph represents gasoline consumption when driving a certain distance in km.  What is the meaning of the slope?

• The tank started with 50 L of gasoline

• the amount of gasoline consumed per km driven

• the distance it takes to lose a Liter of gas

• the gasoline is leaking because the slope is negative.

• A
• B
• C
• D

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

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.

The following computer output describes the relationship between y = height (in cm) and x = foot length (also in cm) for 12 randomly selected students from the British Census @ Schools database. The scatterplot for this relationship show a roughly linear shape. Which of the following is the correct interpretation of the number s = 7.39858?

• For each one-centimeter increase in foot length the model predicts an increase in height of 7.39858 centimeters.

• If we use the regression equation to predict height from foot length, our predictions will be, on average, off by 7.39858 centimeters.

• The typical difference between the height of a student and the mean student height is 7.39858.