Choosing the Best Model — Unit test Answers

The weight (in pounds) and height (in inches) for a child were measured every few months over a two-year period. The results are given in the table.

The arm span and foot length were measured (in centimeters) for each of the 19 students in a statistics class and displayed in the scatterplot. An analysis was completed and the computer output is shown. PredictorCoefSE Coeft-ratiopConstant-7.6112.5672.9650.046Arm span0.1860.0355.3770.000S = 1.61R-Sq = 63.0%R-Sq(Adj) = 62.7%

A nutritionist collects data from 25 popular breakfast cereals. For each cereal, the number of calories per serving is plotted on the x-axis against the number of milligrams of sodium on the y-axis. The value of r for the resulting scatterplot is 0.83. How would the value of the correlation coefficient, r, change if sodium was plotted on the x-axis and calories plotted on the y-axis?

Data was recorded for the temperature, in degrees Celsius, of a cup of coffee over a 30-minute period. Given the regression equation, , what is the predicted temperature after 3 minutes?

A popular social media platform has begun offering stock shares to the public. In the past 2 years, the price of the stock has generally increased. An investment specialist gathers data on the stock price during the past 2 years and creates an exponential model for estimating the stock price based on the number of weeks after the first public offering.

Market researchers were interested in the relationship between the number of pieces in a brick-building set and the cost of a set. Information was collected from a survey and was used to obtain the regression equation ŷ = 0.08x + 1.20, where x represents the number of pieces in a set and ŷ is the predicted price (in dollars) of a set. Which statement best describes the meaning of the y-intercept of the regression line?

A newspaper collected information on schools in its circulation area in order to compare their quality. Two measures the newspaper collected for each school, mean class size and mean score on a statewide reading exam, are shown in the scatterplot.

Water is poured into a large, cone-shaped cistern. The volume of water, measured in cm3, is reported at different time intervals, measured in seconds. The scatterplot of volume versus time showed a curved pattern.

A sports statistician was interested in the relationship between game attendance (in thousands) and the number of wins for baseball teams. Information was collected on several teams and was used to obtain the regression equation ŷ = 4.9x + 15.2, where x represents the attendance (in thousands) and ŷ is the predicted number of wins. What is the predicted number of wins for a team that has an attendance of 2,100?

College administrators at a small, private college noticed that students who had higher high school GPAs tend to have higher college GPAs.

Janice is considering buying a new home. She wants to estimate the monthly utilities (heating and air conditioning). She figures that the utilities are dependent on the size (square footage) of the home. She collects data on 10 homes in the neighborhood and finds a linear model to give the relationship between the size of the home and the monthly utilities. The equation of the line is ŷ = –8.1 + 1.91x, where ŷ is the mean monthly cost in utilities and x is the square footage of the home. The residual plot is shown.

How is the distance from the sun for planets in our solar system related to the mean temperature of each planet? To find out, scatterplots that relate the distance of each planet (including Pluto) from the sun in millions of miles and the mean planetary temperature in Kelvin were created. Some of the scatterplots use the natural log to transform one, or both, of the variables.

A guidance counselor wants to determine if there is a relationship between a student’s number of absences, x, and their grade point average (GPA), y. The data that were collected are displayed in the scatterplot and the least-squares regression line was calculated. One student with 2 absences has a GPA of 1.8. This point is circled on the graph.