6.7 scatter plots and line of best fit | PDF - Free Printable

Here are the solutions to the problems on your worksheet.

1. MUSIC (Scatter Plot Prediction)

Step-by-step:
* Identify the trend: Look at the dots on the graph. As the years go by (moving right), the number of CDs sold goes down (moving down). This is a "negative correlation."
* Find the rate of change: Let's pick two clear points to estimate the line.
* In 1999, sales were about 950 million.
* In 2003, sales were about 750 million.
* That is a drop of 200 million over 4 years.
* $200 \div 4 = 50$. So, sales drop by about 50 million each year.
* Predict for 2006:
* From 2003 to 2006 is 3 more years.
* If it drops 50 million per year: $3 \times 50 = 150$ million drop.
* Start at the 2003 value (750) and subtract the drop (150).
* $750 - 150 = 600$.

Final Answer: About 600 million CDs.

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2. FAMILY (Scatter Plot & Relationship)

Step-by-step:
* Plotting: You need to put "Income" on the bottom axis (x-axis) and "Cost" on the side axis (y-axis). For example, find 18 on the bottom and 10.70 on the side, and put a dot there. Do this for all pairs.
* Describe the relationship: Look at how the dots move. As the income numbers get bigger (move right), the cost numbers also get bigger (move up).
* Conclusion: When both variables go up together, it is a positive relationship.

Final Answer: There is a positive relationship (or positive correlation). As family income increases, the predicted annual cost for raising a child also increases.

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3. Line of Best Fit (Table Data)

Step-by-step:
* Plot the points: Put the X values on the bottom and Y values on the side.
* Points: $(-2, 2), (-1, 0), (0, -2), (1, -4), (2, -6)$.
* Draw the line: Notice that every time $X$ goes up by 1, $Y$ goes down by 2. The dots form a perfectly straight line. Draw a line connecting them.
* Find the Equation ($y = mx + b$):
* Slope ($m$): The rise over run. To get from one point to the next, you go down 2 and right 1. So, $m = -2$.
* Y-intercept ($b$): Where does the line cross the vertical y-axis? It crosses at $-2$ (when $x=0$). So, $b = -2$.
* Combine them: $y = -2x - 2$.

Final Answer: The equation is $y = -2x - 2$.

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4. EDUCATION (Study Hours vs Grade)

a. Scatter plot and line of best fit:
* Plot the points with Study Hours on the x-axis and Grade on the y-axis.
* Draw a straight line through the middle of the cloud of dots. It should start near $(0, 75)$ and end near $(5, 95)$.

b. Equation for the line of best fit:
* Let's estimate using two points on our imaginary line: $(0, 75)$ and $(5, 95)$.
* Slope ($m$): Change in $y$ divided by change in $x$.
* $(95 - 75) / (5 - 0) = 20 / 5 = 4$.
* Y-intercept ($b$): The grade when study hours are 0. Looking at the data, it is around 75.
* Equation: $y = 4x + 75$.

c. Predict the grade for 6 hours:
* Use the equation from part b: $y = 4(6) + 75$.
* $4 \times 6 = 24$.
* $24 + 75 = 99$.

d. Could this go on forever?
* Reasoning: In math, lines go on forever. But in real life, grades have a limit. The highest possible grade is usually 100%. If you plug in a huge number for hours (like 100 hours), the equation would give a grade of 475%, which is impossible. Also, studying too much leads to tiredness, which might lower grades.

Final Answer:
b. $y = 4x + 75$ (Note: Answers may vary slightly depending on exactly where you draw your line, e.g., $y = 3.5x + 76$ is also acceptable).
c. 99%
d. No. Grades cannot exceed 100%, and eventually, fatigue would prevent scores from increasing indefinitely.