We know that E is still equal to actual cost. So I'm looking at the residuals blood, and it looks like when the tempest 10 F residual is about negative six or negative seven. When the temperature is standing leash very night, we're gonna have to approximate right, and we're literally just reading off the value of the residual from the blood. We need to use a residual splutter and find the value of the residual. We know that at this temperature predicted cost. Find the actual heating cost for that month. So we just plug in the value for temperature and we get $111 70 cents for the next question. I'm using the original form off the linear model here, and we want to calculate predicted cost when the temp is equal to 10 F. So for the next question, if temp is equal to 10 F, what is the value off the predicted course? Here we use our linear model. For temps close to freezing, predicted course is greater than actual cost. Therefore, predicted cost must be bigger than actual course. If that is negative, that means it's less than zero. So that means if the residual, which is equal to actual cost minus predicted cost. Now, if you look at the residual splatter for temperatures close to 32 degrees, the values of the residuals are always negative. So when we see freezing, we mean the freezing point or freezing temperature off water, which is 32 degrees Fahrenheit. So next question is what happens to predicted cost when the temperature is close to freezing. So what does the Y intercept mean in this context? Well, we already know that the Y intercept is equal to 1 33 It's the value off the predicted cost when temperature is equal to zero. Note how a negative slope translates into a decrease in the cost. Increase in temperature or equivalently using dish model cost depreciates by 2.13 for 1 F. This means that under this model cost changes by negative 2.13 for 1 F. X variable is the temperature, the slope is negative 2.13 and the UAE inter ship it's 133 so the slope is negative 2.13. Predicted cost is equal to negative 2.13 I'm still them English 1 33 Note that this is an equation off a line in slope intercept form. The Slope M can be interpreted as the change in wine Boo one unit increase in X The Y intercept be Is the value off why when x is equal to zero? And you could see that by looking at the equation in slope intercept form when x zero Why is equal to being so? The first question is, what does the slope mean In this context? Let's rewrite our linear model in an equivalent form. It's an equation off a line in slope intercept form Y in X or your valuables and Mr Slope be this Dewie Inter ship. So from algebra, we know that equation y equals MX plus being. In order to answer the first two questions, let's do a quick algebra review. Predicted cost equals 1 33 minus 2.13 times temperature and the residuals blood for the data. So for this particular problem, Ah, home owner would like to estimate its monthly, he think cost using the average daily temperature Costis in dollars temperatures in degrees fire night.
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