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### Course: Statistics and probability > Unit 5

Lesson 3: Introduction to trend lines- Fitting a line to data
- Estimating the line of best fit exercise
- Eyeballing the line of best fit
- Estimating with linear regression (linear models)
- Estimating equations of lines of best fit, and using them to make predictions
- Line of best fit: smoking in 1945
- Estimating slope of line of best fit
- Equations of trend lines: Phone data
- Linear regression review

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# Equations of trend lines: Phone data

Paige collected data on how long she spent on her phone compared to how much battery life was remaining (in hours) throughout the day. Here is the data:

Time spent on phone (hours) | |||||||||

Battery life remaining (hours) |

She then made this scatterplot:

Now she wants a trend line to describe the relationship between how much time she spent on phone and the battery life remaining. She drew three possible trend lines:

## Want to join the conversation?

- How do you find the slope of the graph?(19 votes)
- Find two good points and count change in y (rise)/change in x (run)(19 votes)

- I do not understand how the last one is 11.7 I got 11.8?(11 votes)
- The trend line is 𝑦 = −0.75𝑥 + 9, where 𝑥 is the time spent on the phone (in hours) and 𝑦 is the expected battery life remaining (in hours).

Paige wants to turn her phone off when there's 15 minutes of battery life remaining.

15 minutes = 1∕4 hours ⇒ 𝑦 = 1∕4 = −0.75𝑥 + 9 ⇒

⇒ 𝑥 = (1∕4 − 9)∕(−0.75) = 11.6666... ≈ 11.7

So, Paige can use her phone for approximately 11.7 hours before she needs to turn it off.(20 votes)

- I don't get the rounding thing what do you have to round?(9 votes)
- Yes but I did the rounding and it was wrong. all the rounding did not work and i did exacts and i got them all right. if i rounded then it came up wrong.(7 votes)

- I still don't understand how to find the slope of a scatterplot when answers are not provided? How do you get the slope-intercept equation if the values are all over the place?(10 votes)
- You don't have to find the slope-intercept equation for the points. You need it for the trend line.(4 votes)

- i'm finding it hard to find the numbers that the line goes through. for example it says "the line goes through (0,9) and (4,6). where did these numbers comes from and how were they spotted. please help me with some steps or anything...(7 votes)
- The coordinates were on the purple line. If you look at the y-intercept, it is (0,9). If you go down to the next whole number point, it is (4,6).(5 votes)

- why was this insanely difficult for me? the estimating equations of lines took me an hour, and I didnt even get it done!(8 votes)
- How do you get 15 to be 1/4's?(5 votes)
- All our other values are in hours, so we would like to express 15 minutes in hours. Since there are 60 minutes in an hour, 15 minutes = 15/60 hours. Dividing top and bottom by 15 gives us 1/4.(5 votes)

- I am not sure I understand this right: if I do not use the phone at all I have 9 hours of battery left. If I then use it for 9 hours I still have circa 2 hours of battery left … ?

If beta (the thing in front of x) is smaller than one that would imply that the phone battery drains slower when in use then when in standby … that makes no sense!(4 votes)- y slope actually and technically means not the actual remaining battery life but the "predicted" one based on usual usage patterns of a user by a manufacturer, I guess.

and the wording of left battery life made me confused too since this could imply a sort of futuristic ultra battery which may run infinitely as it always has an amount of battery left after an hour of usage, no matter how small it is!

if y slope was tagged as "expected battery life", it might give no confusion.(6 votes)

- I don't understand trend lines or slope graphs. It is all too confusing.(6 votes)
- Sometimes when i don't understand things I have to go back and revisit videos on the subject.

https://www.khanacademy.org/math/algebra/two-var-linear-equations/slope/v/slope-of-a-line Go back over those and click on the videos of parts you do not understand. Hang in there, you will get it. :)(2 votes)

- Hi, where can I find the lesson that goes into details as to the maths behind the calculation done above? That is, if line goes thorugh (0,9) and (4,6), then the slope is equal to (6-0)/(4-9) = -0.75? How do we know which way to do the substitution?

My calculation would have been to say that we know that in y=ax+b, b has to be equal to 9 given that it's the intercept. From there, we know that 6 = 4a + 9, so we can derive that a = -0.75. But I want to learn the technique used above.(5 votes)- From trigonometry, slope of the line is nothing but the height divided by base in a right angle triangle. So let say there are two points (0,9) and (4,6), imagine a right angle triangle created out these two points, now the base is (x2-x1) and height is (y2-y1) and hypotenuse the is line itself. Hence the slope will now be (y2-y1)/(x2-x1).(2 votes)