Worksheet: Scatter Plots and Lines of Best Fit

In this worksheet, we will practice drawing lines of best fit for a scatter plot and using them to interpret and make predictions about the data.

Q1:

The following scatter diagram shows the test results of two exams for a class of 26 students. If Sophia got 84 on exam 1, which of the following would you expect to be her score for exam 2?

  • A92
  • B70
  • C50
  • D86
  • E60

Q2:

A linear regression model of the form 𝑦=𝑎+𝑏𝑥 has been fitted to the data shown. Which of the following statements are true about the values of 𝑎 and 𝑏 in the fitted regression model?

  • A 𝑏 > 0 , 𝑎 > 0
  • B 𝑏 < 0 , 𝑎 > 0
  • C 𝑏 < 0 , 𝑎 < 0
  • D 𝑏 < 0 , 𝑎 = 0
  • E 𝑏 > 0 , 𝑎 < 0

Q3:

The following scatterplot shows the heights and weights of 24 students in a class. Use the scatter graph to determine which of the following would be the best estimate for the weight of a person who has a height of 150 cm.

  • A53 kg
  • B100 kg
  • C40 kg
  • D36 kg
  • E30 kg

Q4:

A linear regression model of the form 𝑦=𝑎+𝑏𝑥 has been fitted to the data shown. Which of the following statements are true about the values of 𝑎 and 𝑏 in the fitted regression model?

  • A 𝑏 > 0 , 𝑎 = 0
  • B 𝑏 < 0 , 𝑎 < 0
  • C 𝑏 < 0 , 𝑎 > 0
  • D 𝑏 > 0 , 𝑎 < 0
  • E 𝑏 > 0 , 𝑎 > 0

Q5:

How useful would a line of best fit be for this scatterplot?

  • Anot useful at all since the data is not linearly correlated
  • Bvery useful since the line of best fit will describe the data accurately
  • Cjust as useful as the data itself since the line goes through every data point anyway

Q6:

Which line fits the data graphed?

  • ANone of the lines fit the data.
  • B 𝐶
  • C 𝐴
  • D 𝐵

Q7:

The scattergraph shows the body mass, measured in kilograms, against the average brain mass, measured in grams, for 15 species of mammals.

Give the approximate brain mass of the point that is most likely to represent an outlier.

  • A700 g
  • B450 g
  • C520 g
  • D 1,300 g
  • E50 g

Which species of mammals do you think this point is most likely to represent?

  • AElephant
  • BChimpanzee
  • CHuman
  • DCow
  • EHorse

Q8:

How useful would a line of best fit be for this scatter plot?

  • Anot useful at all, since the data is not linearly correlated enough to apply a line of best fit
  • Bvery useful, since it will be close enough to the data points to give reasonable approximations
  • Cjust as useful as the data, since the line goes through every data point anyway
  • Dpossibly useful, as there is a pattern but the data points do not match up that well

Q9:

The scattergraph shows a set of experimental data (purple). Simon fits two possible regression models to the data: a quadratic model of the form 𝑦=𝑎𝑥+𝑏𝑥+𝑐 (orange) and an exponential model of the form 𝑦=𝑎𝑏 (green). Which of these two models appears to be a better fit for this data set?

  • Athe quadratic model
  • Bthe exponential model

Q10:

The four scatterplots show the same two variables 𝑥 and 𝑦 but transformed in different ways. Based on these scatterplots, what type of regression model would be most appropriate to model 𝑦 in terms of 𝑥?

  • Aa linear model
  • Ba quadratic model
  • Can exponential model

Q11:

Michael made a pot of tea and then recorded its temperature, in degrees Fahrenheit, over the following hour. Michael concluded that the temperature 𝑇 of the tea, 𝑥 minutes after it is made, can be modeled by the exponential regression model 𝑇=190×0.985.

Use the model to estimate, to the nearest degree, the temperature of the tea after 25 minutes.

  • A 1 3 0 F
  • B 1 6 5 F
  • C 1 1 0 F
  • D 1 2 0 F
  • E 1 2 5 F

Q12:

Oscar collected data on the age of a group of children and the amount of allowance they received each week. He then fitted a linear model to this data set. Oscar then calculated the residual for each point and plotted them as shown.

Does a linear model appear to be appropriate for this data set?

  • Ano
  • Byes

Q13:

The scattergraph shows a set of experimental data (purple). Simon fits three possible regression models to the data: a linear model of the form 𝑦=𝑎+𝑏𝑥 (blue), a quadratic model of the form 𝑦=𝑎𝑥+𝑏𝑥+𝑐 (orange), and an exponential model of the form 𝑦=𝑎𝑏 (green). Which of these models appears to be the most suitable fit for this data set?

  • Athe exponential model
  • Bthe linear model
  • Cthe quadratic model

Q14:

The scatterplot shows the average life span (yr) versus oxygen consumption (cubic centimeters per gram of body weight) of 26 different species of mammals. What type of model would be the least appropriate for modeling this data?

  • Aa linear model
  • Ba quadratic model
  • Can exponential model

Q15:

The four scatterplots show the same two variables 𝑥 and 𝑦 but transformed in different ways. Based on these scatterplots, what type of regression model would be most appropriate to model 𝑦 in terms of 𝑥?

  • Aan exponential model
  • Ba linear model
  • Ca quadratic model

Q16:

Emma collected data on the age of a group of children and how many hours they spent doing homework each week. She then fitted a linear model to this data set. Emma then calculated the residual for each point and plotted them as shown.

Does a linear model appear to be appropriate for this data set?

  • Ano
  • Byes

Q17:

The four scatterplots show the same two variables 𝑥 and 𝑦 but transformed in different ways. Based on these scatterplots, what type of regression model would be most appropriate to model 𝑦 in terms of 𝑥?

  • Aa quadratic model
  • Ba linear model
  • Can exponential model

Q18:

Given that the 𝑥- and 𝑦-axes are at the same scale, which of the following are possible values of 𝑎 and 𝑏 for the linear regression model shown in the diagram?

  • A 𝑎 = 0 , 𝑏 = 1 . 9
  • B 𝑎 = 4 . 6 , 𝑏 = 1
  • C 𝑎 = 0 , 𝑏 = 1 . 9
  • D 𝑎 = 1 0 . 1 , 𝑏 = 3 . 6
  • E 𝑎 = 9 . 4 , 𝑏 = 2 . 8

Q19:

Which line fits the data graphed?

  • A 𝐶
  • B 𝐴
  • C 𝐵

Q20:

Which line fits the data graphed?

  • A 𝐴
  • BNone of the lines fit the data.
  • C 𝐶
  • D 𝐵

Q21:

Which line fits the data graphed?

  • AA
  • BC
  • CNone of the lines fit the data.
  • DB

Q22:

How useful would a line of best fit be for this scatterplot?