How to Make Predictions From a Scatter Plot

Make a scatter plot and make predictions. So the first problem, in this problem, it gives us the water temperatures of various depth in a lake are given. So we have our water depth and then the temperature, so when the water depth is zero feet, the temperature is 74 feet and so on. So with this information, we need to one, make a scatter plot using the data then draw a line of best fit, then we need to write an equation for the best fit and last, we need to use the equation to predict the temperature of a depth of 60 feet.

So first, we need to make a scatter plot using the data, so a scatter plot is used to show the relationship between two sets of data. So our two sets of data would be the water depth and the temperature and then in the scatter plot, the two sets of data are graphed as ordered pairs on a coordinate plane. So for instance, water depth would be your x value and then the temperature would be your y value. So your ordered pair would be (x, y) right? Our first order pair then would be 0, 74, our second would be 10, 72 and then 20, 71 and so on.

Now, to make a scatter plot using this data, we’re going to — we graph each of the data points right? So we add our first set of data which we said was 0, 74. So we have the water depth that was zero and the temperature is 74. So we just went ahead and plot this in. So our first set was zero is the water depth and 74 is the temperature and then we plotted it and so forth. After we have our data point, we need to draw a line that passes through or is very close to most of the data point and this is called our best fit line. So the best fit line passes through or is very close to most of the data points.

So when you draw the best fit line, a good way to do it is to estimate a line that best fits, so you can like lay of rulers edge over the graph and adjust it until it looks close to all the points. So you just use your ruler and you want to make sure that it gets as close as possible to all the points, so obviously, it’s the best fit. It’s not going to touch all your points but it should be as close as possible to most of your data points.

So here we have our best fit line which is right here. Now, after we have our best fit line, now we need to write the equation for this best fit line. So to write the equation of a straight line, we need two points. So we need two points on the line. So the line of best fit passes through 25 and 64, and 35 and 58. So we’re going to use these points to find our slope. So we’re going to use 25 and 64 and then we’re also going to use 35 and 58 based on our best fit line. So our first one, (x, y) or x1 and y1 is going to equal 25 and 64. And then x2 and y2 is going to equal 35 and 58.

So now, the definition of a slope is m = (x2-y1)/(x2-x1), so this is the definition of a slope. So we need to substitute our values, so we’re going to go ahead. And y2, we said is 58 minus y1 which is 64. And that’s going to be divided by x2 is 35 minus x1 which is 25. So we go ahead and solve that and we get -6 / 10 and then we simplify and then we get negative -3/5. So the slope of our line is -3/5, so this would be our slope.

So write the equation of the line, we need to find the Y intercept. So to find the equation of the line, we need to find the Y intercept, the point where the line cuts the Y axis. So let’s look here at our best fit line. The Y intercept is where the best fit line crosses the Y axis. So this would be the Y intercept. So here; our y intercept would be 79. So the line of best fit cuts the axis at 79. So now, we’re going to use this slope in Y intercept to write our equation, so I’m going to just move back down here. To find the slope intercept form, so now we’re looking for the slope intercept form. We’re going to use the equation y=mx+b. So we know that we’re looking for y. We know that m is our slope and we know our slope is -3/5. x+b and we’re going to substitute b for 79 because that’s where what we said up here where the Y intercept crosses or the best fit line crosses the y axis at 79.

So we substituted m for -3/5 and b for 79 and now, we simplify and we get y=m -3x/5+79. So the equation for the best fit line is y = -3x/5+79 and that is the equation for our best fit line.

All right. Now, let’s go to number three where we have to use this equation to predict the temperature of a depth of 60 feet. So the equation of the best fit line can be used to predict these values. So let’s take our equation for best fit line which we said was y = -3x/5+79 and now, we’re going to substitute x for 60 because we want 60 feet right? So we have y= -35*60+79 and then we simplify and we get y= 43. So the temperature of the depth at 60 feet will be about 43 degrees Fahrenheit.

So remember that a scatter plot, we go back to our first part, a scatter plot is a graph that shows the relationship between two sets of data. So in a scatter plot, we enter two sets of data, the water depth and the temperature and in this type of graph, two sets of data are graphed as ordered pairs on a coordinate plane. So remember, when our water depth was zero, our temperature was 74 right? And those are set as ordered pairs.

The line that passes through or is very close to most of the data points is called the best fit line. The slope of a straight line is given by the equation m=(y2-y1)/(x2-x1) where x1 and y1 and while x2 and y2 are two points on the line. The equation of a straight line is y=mx+b and that’s the slope intercept form. The equation of the best fit line can be used to predict our values just like we did in number three.