Everybody. My name is Colin. And let's go ahead and jump into this problem that deals with corn and weeds and whether or not there is a potential relationship between on increase in weeds per meter and an increase or decrease in the output of corn. So part they asked us to analyze this scatter plot that we've got here and describe the relationship. There were the potential relationship between the corn yield and weeds per meter so we can see from those data points there and from that regression line that they've got drawn in there.
We've got what I would describe as a week linear relationship between the two variables. So you can see that big because there is a general downward trend down to the right negative slope. Um, we can kind of see that there is a potential relationship between these two variables. It is not super strong, but it is there, and we'll get into how strong it is later on. So let's go ahead and jump now into part B or asked to simply find ah, that regression the least squares regression line equation from that many tap output.
And so if you see my earlier videos from this chapter where we talk about how to find Ah, that regression line. You'll know that about the overall. Our general equation for your regression line is in the forum. Why equals Alfa plus Beta X? And in this case, we're looking for Alfa, which is the intercept of the regression line, and Beta, which is the slope. And so, in this case, for this problem to find that Alfa value, we're gonna go ahead and look at the Constant Row coefficient column and you'll see that that intercept is 1 66.483 and you'll see that that beta value, which is that same coefficient column but now in the weeds per meter row is negative 1.987 So from this, we get our overall general formula for the the equation of the least squares regression line as 1 66.483 minus 1.987 x.
And just like that off the bat, we've solved parts A and B in part C just asked us to interpret what the slope and the Y intercept mean and constant in context accused me So we were given that our our slope or at beta value waas negative 1.987 And what this just means in context, uh is that we're Look, we're looking for the slope is just the change in corn yield given one additional we'd premier. So basically what? This negative number right here is telling us negative 1.987 is telling us that the corn yield decreases by 1.987 bushels given on additional we'd per meter and that Alfa value that we've got or the intercept apologize. I'll go ahead and draw better Alfa than that, Which was that 1 66 point for a three number? When we analyze that, that's just are expected corn yield when we there are zero weeds per meter. And so that just means that if there are zero weeds per meter, um, we're going to have an estimated corn yields of 1 66.483 And when you think about it, this kind of makes sense. We have, ah, high corn yield when they're zero weeds per meter.
And intuitively, we know that the addition of weeds may hinder the growth of corn and eso. You can see that the slope is negative or the amount of corn decreases as you increase the amount of weeds per meter. But now we move on the part D, which is we are asked to carry out a test at the Alfa equals 0.5 level of significance to answer this question. And so this is where we're going to now start to get into our no hypothesis test. So for part D, we're going to set up two different hypothesis.
First, we're going to have the no hypothesis on. That's just going to be, Ah, that beta, the slope of the regression line is zero on what this means is, is our We're looking at whether or not we reject this null hypothesis. So obey the equal zero. That means the slope zero and there is no relation between the corn yield and the number of weeds in a particular plot. And so then we'll be looking at that against the help.
The alternative hypothesis that beta does not equal zero r beta is less than zero. Excuse me. Um, because if you read that problem, you'll see that we're looking at, whether or not more weeds reduced corn yield on we're going to be doing this is they ask for at that Alfa off 0.5 level of significance, I'll point out that this outfit value right here is a different Alfa value than the one that we calculated. Our we looked at in the progression announced that this problem are reminded that we're now doing a hypothesis test and the number of degrees of freedom. We saw that there were 16 corn plots plan sets.
The degrees of freedom is always end minus two or the number off trials or plots minus two. We will go with a degrees of freedom here for 14 for this test. So first, we're gonna go ahead and calculate our tr critical, uh, value our T statistic on to do that. We're going to, uh, do beta. We're going to ah, subtract are no hypothesis value of beta or zero from our given beta negative 1.987 And we're going to put that all over the standard deviation from this problem or R s output from that regression analysis which is just going to give US negative 1.987 all over 0.5712 Which will see is that Sigma value? In the mini tap output, we calculate that we get a T value of negative 1.923 and now we're going to go ahead and use that to find RPI value, which is what's going to we're going to compare to Alfa to see whether or not we reject the null hypothesis.
So are inputs for that p value. We are looking at a T star R R T Value T statistic of negative 1.923 We're looking at 14 degrees of freedom and because we just need a large number, I'm going to just pick 10 million. Um, are negative 10 million any value of any large value and will work here. But I'm going to pick negative 10 million, and I'm going to go ahead and run eight a test on that you can use Excel. You can use an online TI calculator or you can use a table on.
When you do that, you get a P value of zero point are sorry 0.0.375 and So that's what we're going to compare. Teoh Alfa Value that we started with at the beginning and sends 0.375 is less than 0.5 You'll remember from the rules of these tests, you know that we can reject that. No hypothesis. And since we reject the null hypothesis and are no hypothesis was that the, uh, more weeds do not reduce cornfield or more weeds do not impact corn, yield it all. We can reject that that that idea.
There is no correlation between weeds and corn yield and say that there is, in fact, sufficient evidence to support the claim that weeds that the increase in weeds are more weeds in a certain plot do reduce the corn yield..