All right, you guys. So for questions 17 here let's go and jump right on and I'm gonna go ahead and solve the entire problem using a google sheet and so let's go ahead and start there. That's starting with google. She does start a bit slower as you do have to input your own X and Y values. Let's go and do that. I'm going to take the X and Y values directly from the problem and we'll go from there. Mhm. So it does take an extra second but trust me it is worth it. Mhm. All right, so those are the heights and now let's see the circumference is right. Mhm. Mhm awesome. Okay, cool. And so now what we need to do is we need to part a which is to find the least squares regression line. Okay, so all I need to do here is very symbolizing to highlight the data and go insert chart and it does Perfect. Okay, it does give me a nice little scatter plot here. If it doesn't give you a scatter plot, not to worry. Um Yeah, it doesn't give you a scatter plot. Not to worry. It will you can make edits on that scatter plot with fairly basic ease here. Um Hold on I'm going to fix the window really quickly, it's not quite the size that I would like it to be perfect. Okay, cool. And so I'm gonna move my chart down here and actually make it a tad smaller as well. So I'm trying to fix my workspace a little here. Perfect. Okay, cool, so there is my chart. Okay so if so if you want to edit your chart first off, you just click on that the three dots hit edit chart. Um And sometimes it won't show up is scatter plot that shows it was like a hissed a gram or something or a column chart. If that happens, no big deal, just click on that, the type of chart and then just click on the scatter plot there. Okay um and before we're able to find the least squares regression line, the good thing is google sheets, do the whole thing for us. You do want to make sure that these two boxes down here and check they already checked for me. So that's good. The next thing we're gonna do is this I'm gonna go to customize and then I think it's series and I think that's right. Yes. Okay, serious. Customize serious. Okay and um and the series are going to scroll down just a touch and you're going to click on trend line. Okay. And there is the least squares regression line but we do need to find the equation as well. So there are equation is right is you can actually find the equation in the label. So the label right now it's not labeled as anything. You can label it with the equation itself and there is our equation. Very good. So that is um that's very very important that we do need to have that equation. Okay so that's good and that is um part a right there. I'm interpreting the slope and y intercept. So our slope means 0.183. So basically what that means is this when the height increases by one inch? Okay, so when the explanatory available variable increases by one, our explanatory available right now is height. So when our height increases by one inch interest, you need to measure that means our head circumference should increase by 0.183 uh inches as well. So for you will get a 0.183 increase in circumference for every increase, one inch increase in height. That is what the slope means. The why the intercept is actually in this case, the y intercept is not quite uh appropriate to interpret at this point because the y intercept occurs when our x value is zero. What it makes sense for a child to have a height of zero? No it does not does not make sense for that to happen. So we would actually say I'm interpreting in this scenario, interpreting the Y intercept would not be appropriate because you don't have a child with height zero. Um Okay so that's part of the part c Um we want to use the equation to predict for when a child is 25 in tall. Um so yeah so that's gonna be right over here. So I noticed we we already have 25 actually actually have a data point for 25 but let's go ahead and see um Our guest list we're going to make a prediction. Um So we're going to make a prediction here for 25 And let's see what happens here. So we're just gonna go ahead and uh input 25 more equations. So let's go and start typing our equation. I'm gonna start by doing equal sign in a new cell. I'm gonna go start typing in the equation and that X. Is right next to it. So I'm going to go times 25 because 25 is our input and then we're gonna add 12.5 And are predicted height is a touch over 17. Okay so we predict a touch over 17 and then this is um looks like this is going to be above average. How do I know that? Um This is gonna be uh oh I'm sorry I skipped part right there. Okay so that's part C. Right there. Part D. Is it wants us to compute the residual. So all we have to do is find the difference between um finally just between our actual value or predicted value. Okay so predicted value was this one. So I started by typing new cell equals um you forgot the labour residual. So this is our residual, it's a residual equals so type equals Um are predicted value minus our actual value and are residual is 0.175. And so um this is above average because that's positive. That is going to be above average. That takes care part d draw the least squares. Regression line. Got it. Um We already did that And then um no. Okay cool. And so then it wants us to notice this actually wants us, we have two instances where have 26.75. Um But even though they're both these two Children here are the exact same height. Um Their head circumference is slightly different. How can this be? Well it just it kind of makes sense right because not every person is exactly the same and that's possible because natural variable variability happens in datasets especially when it comes to human beings. So yeah that's just normal. I mean natural variability happens is what I might say. Um and then for part G what we would say is it would not be reasonable to predict the head circumference of a child who is 32" tall. Are data set works is strictly between 24.5 and 27.7 looks like 27.75. And so we do not want to predict data that is outside our data set because we cannot guarantee that the relationship will remain the same outside of our data set. So that would be inappropriate to predict um to use this regression line to predict Um the head circumference of a child who is 32" tall