Use the table that shows the life expectancy for people born...

Use the table that shows the life expectancy for people born in various years.
$\begin{array}{|c|c|c|c|c|c|}\hline 1950 & {1960} & {1970} & {1980} & {1990} & {2000} \\ \hline 68.2 & {69.7} & {70.8} & {73.7} & {75.4} & {7.0} \\ \hline\end{array}$
Find a prediction equation.

Key Concepts

Linear Regression

Linear regression is a statistical method used to model the relationship between one independent variable and one dependent variable by fitting a linear equation to observed data. The equation often takes the form y = mx + b, where m is the slope and b is the y-intercept.

Prediction Equation

A prediction equation is the specific linear equation derived from regression analysis that can be used to estimate the value of the dependent variable based on a given value of the independent variable. It provides a means to predict outcomes beyond the sample data.

Independent and Dependent Variables

In the context of regression analysis, the independent variable is the one that provides input or cause (such as year in this example), while the dependent variable is the outcome or effect (like life expectancy). Understanding which variable plays each role is crucial for correctly setting up the analysis.

Slope and Intercept

The slope and intercept are key components of the linear equation in regression. The slope indicates the rate of change of the dependent variable for a one-unit change in the independent variable, and the intercept represents the predicted value of the dependent variable when the independent variable is zero. These parameters are essential in forming the prediction equation.

Transcript

00:04 All right, having created the scatter plot for this life expectancy data and decided that the correlation is positive in the previous exercise, now we're tasked with finding a prediction equation.

00:18 Well, to find a prediction equation, we need to draw a or estimate a line of fit that would go through these points reasonably well.

00:28 And depending on how you decide to draw that line, you may get slightly different versions.

00:34 Of an equation.

00:36 So i'm going to say, let's say that we connect this point here to this point here.

00:41 To me, those look like they line up pretty darn good.

00:43 And so i'm going to say, let's draw our line, our prediction line, to be this one here.

00:50 And then let's use those two points.

00:52 Remember, this point is the year 1990 with a life expectancy of 75 .4.

00:58 And this point here is the year 1960, with a life expectancy of 69 .7, we're going to use those two points to generate a prediction equation.

01:08 So to get the prediction equation, that's going to be something in the y equals mx plus b form.

01:14 The first thing we need to do is find the m or the slope between these two points.

01:19 So the slope, again, would be y2 minus y1 over x2 minus x1, or the x difference in the y coordinates, and then the difference in the x coordinates.

01:30 Now, in this case, the y coordinates are life expectancy.

01:34 So i'm going to go to my two points, the red one and the green one here, and i'm going to subtract the life expectancy of the first point from the life expectancy of the second point...

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