Jacob is a marathon runner. He wants to know if a relationship exists between male runners’ ages and their marathon times. He used data from the New York City Marathon to create the scatterplot below.Select the trend line and reasoning that would best show the relationship between marathon runners' ages and race times.Group of answer choicesAn exponential trendline is best because older men tend to have much slower running times.An exponential trendline is best because men between 25 and 30 are the fastest. Race times increase for men who are both older and younger than 25–30.A quadratic trendline is best because older men tend to have much slower running times.A quadratic trendline is best because men between 25 and 30 are the fastest. Race times increase for men who are both older and younger than 25–30.A linear trendline is best because it is the simplest model of the relationship between running times and age.

Jacob wants to see if there is a relationship between the speed of a male runner and his age. He collected the age and race time from 27 male runners in a local 200 meter race. His data is depicted in the scatterplot below.Which of the following interpretations does this scatterplot best support?Group of answer choicesThe decreasing exponential trendline is the best choice for this data because older men's running times are exponentially shorter than younger men's times.There is no relationship between men's ages and their running times in the 200 meter race.A linear trendline with a negative slope is the best choice for this data because older men's running times are shorter than younger men's times.The quadratic trendline is the best choice for this data because from Jacob's scatterplot it looks like men around 40 have the slowest running time (the vertex). Men both younger and older than 40 are faster than 40 year olds.A linear trendline with a positive slope is the best choice for this data because older men's running times are longer than younger men's times.

Shondra frequently goes running in the mornings. She recorded the outside temperature and the number of miles for each run. Shondra created the following graph. Which trend line would be most appropriate for her data?Group of answer choicesA positive quadratic trend line.An increasing exponential trend line.A negative quadratic trend line.An increasing linear trend line.A decreasing exponential trend line.

Copy and paste the following data into Excel. Create a scatterplot of the data and use the scatterplot to determine if the data would best be represented by a linear, quadratic, or exponential trendline.x y7.4 5.336.3 11.181.5 9.325.7 12.124.5 13.62.6 12.536.1 9.576.5 9.31253.8 13.972.1 10.25Group of answer choicesExponentialLinearThere is no discernable trend.Quadratic

Christopher has collected data about women's heights and their shoe sizes. He noticed that taller women tend to have larger shoe sizes and shorter women tend to have smaller shoe sizes. Christopher would like to use a trendline to predict the shoe size for a woman that is 70 inches tall.Which type of trendline would be the best choice to model the relationship between women's heights and their shoe sizes?Group of answer choicesA quadratic trendline.An exponential trendline.There is no relationship between women's heights and their shoe sizes.A linear trendline.All of these trendlines would predict the exact same shoe size for a woman that is 70 inches tall.

Three runners competed in a race. Data were collected at each mile mark for each runner. If the runner ran at a constant pace, the data would be linear. A regression line was fitted to their data. Use the residual plots to decide which data set is best fit by the regression line, and then identify the runner that kept the most consistent pace.