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Worksheet: Scatter Plots and Lines of Best Fit

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?

  • A50
  • B60
  • C92
  • D86
  • E70

Q2:

A linear regression model of the form 𝑦 = 𝑎 + 𝑏 𝑥 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:

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

  • A just as useful as the data, since the line goes through every data point anyway
  • B very useful, since it will be close enough to the data points to give reasonable approximations
  • C not useful at all, since the data is not linearly correlated enough to apply a line of best fit
  • D possibly useful, as there is a pattern but the data points do not match up that well

Q4:

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 = 𝑎 𝑥 + 𝑏 𝑥 + 𝑐 2 (orange) and an exponential model of the form 𝑦 = 𝑎 𝑏 𝑥 (green). Which of these two models appears to be a better fit for this data set?

  • A the exponential model
  • B the quadratic model

Q5:

Which line fits the data graphed?

  • A 𝐶
  • B 𝐵
  • C 𝐴

Q6:

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 ?

  • A the exponential model
  • B the linear model
  • C none of the above
  • D the quadratic model

Q7:

Which line fits the data graphed?

  • A 𝐵
  • B 𝐴
  • C 𝐶
  • DNone of the lines fit the data.

Q8:

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.

  • A 100 kg
  • B 30 kg
  • C 36 kg
  • D 53 kg
  • E 40 kg

Q9:

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 = 1 9 0 × 0 . 9 8 5 𝑥 .

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

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

Q10:

Benjamin collected data on the age of a group of children and the amount of pocket money they received each week. He then fitted a linear model to this data set. Benjamin 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

Q11:

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

  • A very useful since the line of best fit will describe the data accurately
  • B just as useful as the data itself since the line goes through every data point anyway
  • C not useful at all since the data is not linearly correlated

Q12:

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

Q13:

Which line fits the data graphed?

  • AC
  • BB
  • CNone of the lines fit the data.
  • DA

Q14:

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 + 𝑏 𝑥 (blue), a quadratic model of the form 𝑦 = 𝑎 𝑥 + 𝑏 𝑥 + 𝑐 2 (orange), and an exponential model of the form 𝑦 = 𝑎 𝑏 𝑥 (green). Which of these models appears to be the most suitable fit for this data set?

  • A the exponential model
  • B the linear model
  • C the quadratic model

Q15:

The scatterplot shows the average life span (years) 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?

  • A a quadratic model
  • B an exponential model
  • C none of the above
  • D a linear model

Q16:

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
  • Ban exponential model
  • Ca linear model

Q17:

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?

  • Ayes
  • Bno

Q18:

Which line fits the data graphed?

  • A 𝐶
  • B 𝐵
  • C 𝐴
  • DNone of the lines fit the data.

Q19:

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

Q20:

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