Hello guys, welcome back and today we're gonna start 7E, interpreting and predicting the linear models. First thing first, we're gonna know how to do the linear models before and then we're able to use an equation to calculate linear models and predict the value of the response. we're gonna do explanatory variables and also the interpolation and the x-provalations and to make the predictions so what's the uh interpreting the slope of intersects of the linear models so two points the slope b tells us the average of the change and response the variables and also each one unit increase or decrease so which is your slope is most important thing And then intercept for A tells us the average values and the response for the variables. And also it's EV for x equals 0. So we need to know what the starting point looks like. So let's start with example 1. The regression line is used to the model's association between the time in hours and groups of students spending study for the...
examination and their work. The equation of the regression will be Mark equal to 30.8 plus 1.62 times time. Write down this intercept. So first one, question A1, 30.8 is intercept.
And question two, interpret the intercept in the constant of the variable. So students who spend no time studying for examination will be scored like 30.8%. So student spent zero time. starting for exam will 10 mark of 30.8 and your slope which is for question B 1 will be 1.62 equal to your slope that means on average students mark will will increase increased by 1.62 for each hour, actual hour of study. Cool!
That's a lot of writings to me actually. We keep going now, we talk about what's the interpolation and the x-populations. Explanation, so interpolation means we're using EVV range of values and generally consider the reliable prediction.
And all set of range of values explained in the EVV, we call this one is called expopulation. And so it's generally considered given. unreliable prediction.
So for example, interpolation is a line to use to make prediction with the range of value of eV. X-population, this line is make the prediction outside the range of the eV, you can say. If some points like around here, that's the X-populations. this straight line here is pretty close to you and then that's the very very interpolation For example, we regression the examination mark 30 hours per hour, which is interpolating. However, we use regression lines and to make the 50 hours study time, it would x populations and x populations, which is less than reliable.
And because we are going beyond the range of the explanatory variables, it's quite possible that association may no longer be a linear. That's very interesting. Now the example 2. So this is about the weight and the kilograms and height in centimeters for the group of students from 163 to 190. So the equation predicts the weight of the students following height.
So we just substitute the 171st. The person who had 170, so the weights will equal to negative 40 plus 0.6 times 170, and that equal to some numbers, and we can use a calculator that was around 62 kilograms. yeah and uh so the width of the height is 65 centimeters which is this is uh interpolation okay for b 65 centimeter weight equal to negative 40 plus 0.6 times 65 that equal to negative one kilograms which is not possible no um and uh that will be extra pollution exploration exploration Thanks. Yeah.
Oh, this is outside the range. So pretty much so that's all you need to know actually and Yeah, and that's it all chapter 7. Hopefully that all makes sense and I will keep uploading the new content and I will see you guys next time