stats ch 6-9

dairy farmers are aware there is often a linear relationship between the age, in years, of a dairy cow and the amount of milk produced, in gallons per week. The least-square regression line produced from a random sample is milk= 40.8 - 1.1(Age). Based on the model, what is the difference in predicted amounts of milk produced between a cow of 5 years and of 10 years?

A cow of 5 years is predicted to produce 5.5 more gallons per week.

Clear-cut harvesting of wood from forests creates long periods of time when certain animals cannot use the forests as habitats. Partial-cut harvesting is increasingly used to lessen the effects of logging on the animals. The following scatterplot shows the relationship between the density of red squirrels, in squirrels per plot, 2 to 4 after partial-cut harvesting, and the percent of trees that were harvested in each of 11 forests.

negative, linear, and strong

For a random sample of 20 professional athletes, there's a strong linear relationship between the number of hours they exercise per week and their resting heart rate. For the athlete in the sample, those who exercise more hours per week tend to have lower resting heart rate than those who exercise less. Which of the following is a reasonable value for the correlation between the number of hours athletes exercise per week and the resting heart rate?

-.87

A researcher in Alaska measured the age (in months) and the weight (in pounds) of a random sample of adolescent moose. When the least-squares regression analysis was performed, the correlation was 0.59. Which of the following is the correct way to label the correlation?

.59

the table shows several values of x and their corresponding values of y. Which of the following is closest to the correlation between x and y?

.98

An exponential relationship exists between the explanatory variable and the response variable in a set of data. The common logarithm of each value of the response variable is taken, and the least-squares regression line has an equation of log(yˆ)=7.3−1.5x. Which value is closest to the predicted value of the response variable for x=4.8?

1.26

Which of the following is the best description of a positive association between two variables?

As the value of one variable increases, the value of the other variable tends to increase.

Which of the following statements about a least- squares regression analysis is true? I. A point with a large residual is an outlier. II. A point with high leverage has a Y value that is not consistent with the other Y values in the set. III. The removal of an influential point from a data set could change the value of the correlation coefficient.

III only

The computer output below shows the result of a linear regression analysis for predicting the concentration of zinc, in parts per million (ppm), from the concentration of lead, in ppm, found in fish from a certain river. Which of the following statements is a correct interpretation of the value J 19.0 in the output?

On average there is a predicted increase of 19.0 ppm in concentration of zinc for every increase of 1 ppm in concentration of lead found in the fish

A botanist found a correlation between the length of an aspen leaf and its surface area to be 0.94. Why does the correlation value of 0.94 not necessarily indicate that a linear model is the most appropriate model for the relationship between length of an aspen leaf and its surface area?

Even with a correlation value of 0.94, it is possible that the relationship could still be better represented by a nonlinear model.

At a large airport, data were recorded for one month on how many baggage items were unloaded from each flight upon arrival as well as the time required to deliver all the baggage items on the flight to the baggage claim area. A scatter plot of the two variables indicated a strong, positive linear association between the variables. Which of the following statements is a correct interpretation of the word "strong" in the description of the association?

The actual time required to deliver all the items to the baggage claim area based on the number of items unloaded will be very close to the time predicted by a least-squares model.

A scatterplot a student heights, in inches, versus corresponding arm span length, in inches, is shown below. One of the points in the graph is labeled A. If the point labeled A is removed, which of the following statements would be true?

The slope of the least squares regression line increases and the correlation coefficient increases.