BIVARIATE DATA ANALYSIS COMMON CORE ALGEBRA I HOMEWORK

Answer Key

  1. A survey was done at Ketcham High School to determine the effect of time spent on studying and grade point average. The table below shows the results for 10 students randomly selected.

Study time

(Hours per week)

2

4

5

7

10

12

14

17

19

20

GPA

(out of 100)

64

71

69

74

81

86

84

94

91

96

  1. Create a scatter plot for this data set on the grid provided. Draw a best fit line through the scatter plot drawn.
  2. Determine the equation for the best fit line for this data set. Use two points from the line you drew in (a) to determine the slope and estimate they– intercept graphically. Round your slope to the nearest tenth and they-intercept to the nearest whole number.

Grade Point Average

  1. Use your answer from part (b) to determine the expected GPA from studying for 8 hours per week. Round your answer to the nearest whole number.

 

  1. Is there a causal relationship between these two variables? If so, which variable causes the other?

 

  1. A survey was done to determine if there was any connection between the price that people pay for their most expensive car and the current value of their house. The results, for eight participants, are given below.

Car Cost,x

(indollars)

11,500

14,750

19,500

26,750

32,900

43,000

45,750

54,500

House Value,y

(in dollars)

160,000

195,000

255,000

400,000

440,000

525,000

475,000

725,000

A computer was used to determine the line of best fit. Its equation was:

y12x33, 766

    1. Use the line of best fit to predict the house value of a person whose most expensive car costs$19,500.

x19, 500

y1219,50033,766$267,766

    1. Was the prediction in (a) an overestimate or underestimate of the actual house value?Explain.
    2. Is there a positive or negative correlation between these two variables?Explain.
    3. Is there a causal relationship between these two variables? If you answer yes, then determine which variable causes the other.If you answer no, then explain a third variable that could be causing both.

No, there is not a causal relationship between the two variables. Although they move in the same direction, a person’s car value does not cause their house value to be higher. The lurking variable is most likely either a person’s income or a person’s wealth. Either of these will cause the two other variables to move in the same direction.

  1. It has been noted that on any given day, there is a strong correlation between the number of ice-cream cones sold and the number of people who go swimming. Is there a causal relationship between the eating ice- cream and going swimming? If not, what could be causing this strong correlation?

No, there is no causal relationship between eating ice-cream and going swimming (although having an ice-cream cone at the pool is awesome). In fact, what causes this strong correlation is the temperature outside. When the temperature outside is hotter, more people go to the pool and more people eat ice-cream.