Line of Best Fit

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Show your work for each problem.

1.
Which description fits a good line of best fit drawn by eye?
1. a)About half of the points are above it and half below, and it follows the trend
2. b)It joins the first and the last data point
3. c)It passes through as many points as possible
4. d)All points are below it
2.
A line of best fit passes through the points $(0, 4)$ and $(5, 14)$ . What is its slope?
3.
A line of best fit passes through $(0, 2)$ and $(4, 10)$ . Find its equation $y = mx + b$ .
4.
Mia's line of best fit is $y = 2x + 3$ , where $x$ is the number of weeks of training and $y$ is the number of push-ups in one minute. What does the slope $2$ mean?
1. a)Each week of training adds about 2 push-ups
2. b)Mia did 2 push-ups at the start
3. c)Mia trained for 2 weeks
4. d)Mia does one more push-up every 2 weeks
5.
A line of best fit drawn by eye passes through $(0, 12)$ and $(4, 4)$ . What is its y-intercept $b$ ?
6.
Is the line $y = x + 1$ a good line of best fit for the points $(1, 3)$ , $(2, 2)$ , $(3, 5)$ , $(4, 4)$ , $(5, 7)$ , $(6, 6)$ ? Count the points above and below it.
7.
A student draws a line through a scatter plot of 8 points. 7 points are above the line and 1 is below it, spread evenly from left to right. How should the student fix the line?
1. a)Make the line steeper without moving it
2. b)Nothing, the line is fine
3. c)Move the line up
4. d)Move the line down
8.
A trend line passes through $(2, 9)$ and $(6, 21)$ . What is its slope?
9.
A line of best fit passes through $(10, 80)$ and $(30, 40)$ . Find its equation $y = mx + b$ .
10.
The mean point of a data set is $(4, 10)$ . Which of these lines passes through it?
1. a) $y = 2x + 3$
2. b) $y = x + 5$
3. c) $y = 2x + 1$
4. d) $y = 3x - 2$
11.
A scatter plot has the points $(2, 5)$ , $(4, 9)$ , $(6, 10)$ , $(8, 16)$ . What is $\bar{y}$ , the y-coordinate of the mean point?
12.
Data: $(1, 3)$ , $(2, 6)$ , $(3, 6)$ , $(4, 9)$ , $(5, 11)$ . A line of best fit with slope $2$ should pass through the mean point. Find its intercept $b$ .
13.
The line of best fit for a phone's battery level $y$ (%) after $x$ hours of use is $y = -12x + 100$ . Interpret it.
14.
For students between 150 cm and 190 cm tall, the line of best fit between height $x$ (cm) and arm span $y$ (cm) is $y = 1.1x - 18$ . What does the intercept $-18$ tell you?
1. a)It has no real meaning: a height of 0 cm is far outside the data
2. b)Everyone's arm span is 18 cm shorter than their height
3. c)A person 0 cm tall has an arm span of -18 cm, a real prediction
4. d)The arm span grows by 18 cm for each cm of height
15.
A line of best fit has slope $-4$ and passes through the mean point $(5, 30)$ . What is its intercept $b$ ?
16.
On a scatter plot, a line of best fit is drawn through the points $(1, 7)$ and $(9, 3)$ on the line. Find its slope and intercept, then the value of the line at $x = 5$ .
17.
The mean point of a data set is $(6, 20)$ . A student's line of best fit passes through $(0, 5)$ and $(10, 30)$ . Does it pass through the mean point?
18.
A café's line of best fit for price $x$ (in dollars) and cakes sold per day $y$ passes through the mean point $(4, 18)$ and through $(8, 10)$ . Find its equation and the number of cakes it predicts at a price of 6 dollars.