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Scatter Plots Practice

Practice Problem #1

A correlation is a measure of the strength of a relationship between two quantities. In your notebook, plot each ordered pair on a graph to make a scatter plot. Then determine the correlation.

Plot each ordered pair.

  • (10, 1)
  • (7, 0)
  • (5, −2)
  • (4, −4)
  • (1, −6)
  • (0, −7)
blank coordinate plane

Answer:

See larger version of Graph #1 here.

Is this a positive or negative correlation?

Answer: Positive

Practice Problem #2

Make a scatterplot of the data in the table and determine the relationship.

Dollars Spent and Gallons Bought
Dollars Spent Gallons Bought
10 2.5
11 2.8
9 2.3
10 2.6
13 3.3
5 1.3
8 2.2
4 1.1
blank coordinate plane

Answer:

See larger version of Graph #2 here.

What type of relationship does the scatter plot show? Positive or negative?

Answer: Positive

Why do you believe the data in this case is scattered and not linear (a completely straight line)?

Answer: All of the points do not appear on a straight line, so it's not linear. The reason it's not linear is because the gas prices tend to fluctuate or change.

Practice Problem #3

Match each graph to the correct correlation.

Graphs:

  1. scatter plot with points in a pattern that moves upwards as you move left and downwards as you move right
  2. scatter plot with points across the coordinate plane in no discernable pattern
  3. scatter plot with points in a pattern that moves upwards as you move right and downwards as you move left

Correlations:

  • Positive
  • Negative
  • No Trend

Answers:

  1. scatter plot with points in a pattern that moves upwards as you move left and downwards as you move right

    Negative

  2. scatter plot with points across the coordinate plane in no discernable pattern

    No Trend

  3. scatter plot with points in a pattern that moves upwards as you move right and downwards as you move left

    Positive

Line of Best Fit Practice

Practice Problem #4

Use the data from the chart and plot the points. Draw the best fitting line and then compute the linear equation for that best fitting line.

Age (months) and Weight (lbs)
Age (months) Weight (lbs)
1 2.5
2 7.5
3 12.5
4 17
6 24.5
8 38
10 49
12 55

First, plot the points and check the answer.

Next, draw a line that best fits the data and check the answer.

Now, we need to compute the linear equation for that best fitting line. Choose two points that fall on the line that you have drawn. Let's use (4, 17) and (12, 55). Use the formula to find the slope.

  • m equals the fraction with numerator y sub 2 minus y sub 1 and denominator x sub 2 minus x sub 1
  • m equals the fraction with numerator blank minus blank and denominator blank minus blank
  • Enter the coordinate numbers into the formula.
  • m equals the fraction with numerator 55 minus 17 and denominator 12 minus 4
  • Simplify.
  • m equals the fraction with numerator 55 minus 17 and denominator 12 minus 4
  • m equals the fraction blank over blank
  • m equals 38 over 8
  • Simplify again.
  • m equals 19 over 4

Next, find the y-intercept using slope-intercept form and one of the points. Let's use (4, 17).

  • y = mx + b
  • blank equals the fraction blank over blank open parenthesis blank close parenthesis plus b
  • Substitute the slope and coordinates into the slope-intercept equation.
  • 17 equals the fraction 19 over 4 open parenthesis 4 close parenthesis plus b
  • Simplify.
  • 17 equals the fraction 19 over 4 open parenthesis 4 close parenthesis plus b
  • 17 = 19 + b
  • ___blank = b
  • −2 = b

Finally, plug the slope and y-intercept into the slope-intercept form to get the linear equation for this line.

  • y = mx + b
  • y equals the fraction blank over blank x plus blank
  • Substitute the slope and intercept into the slope-intercept equation.
  • y equals the fraction 19 over 4 x plus negative 2
  • The equation for our line is:
    y equals 19 over 4 x minus 2

You've completed these review activities!