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The cost of a previously owned car depends upon factors such as make and model, model year, mileage, condition, and whether the car is purchased from a dealer or from a private seller. To investigate the relationship between the car's mileage and the sales price, data were collected on the mileage and the sale price for 10 private sales of model year 2000 Honda Accords (PriceHub website, October $2008 ) .$

a. Develop a scatter diagram with miles as the independent variable.b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?c. Use the least squares method to develop the estimated regression equation.d. Provide an interpretation for the slope of the estimated regression equation.e. Predict the sales price for a 2000 Honda Accord with $100,000$ miles.

a. See scatter diagramb. Negative linear relationshipc. $\hat{y}=8.941-0.026 x$d. Price decreases on average by $\$ 26$ per thousand miles.e. $\$ 6,341$

Intro Stats / AP Statistics

Chapter 12

Simple Linear Regression

Linear Regression and Correlation

Missouri State University

University of North Carolina at Chapel Hill

University of St. Thomas

Idaho State University

Lectures

0:00

04:55

Introduced in the 2000 mod…

04:47

Emily Smith decides to buy…

02:25

Megan, from Exercise 8, de…

In this exercise, we use linear regression to ultimately predict the price for a used car with 100,000 miles on it. Now in the question were given this data for used cars that were given the miles on the cars in thousands and the prices for the cars in thousands. And for part, they were asked to develop a scatter diagram with miles as the independent variable, which means that miles is on the X axis. This is straightforward to do in Excel. We just simply select the data. Both columns, click on, insert, pick this type of chart here, click on scatter and we see this relationship. Now we can make this chart a bit more useful by eliminating some of the domain on the X and Y axes. So if we right click on the chart format chart area, go to church options and let's select the vertical axis first. So we'd like that to go from about 4 to 8. We click the fourth option here. Access options and let's give it a minimum of four and we can do the same thing for the X axis. Again we go to access options horizontal axis and we want to go from 5200 and 40 and there we have it. And so that is part A. If you're going to hand in a chart, of course you want to put a title on it and label the X and Y axes for part B. Were asked what the scatter tells us about the relationship between the two variables and we can see that it indicates a fairly linear pattern with a negative slope. So it suggests that price is negatively correlated with miles. There is a negative linear correlation between the two variables and next for part C. We were asked to use the least squares method to develop the estimated regression equation pleasing this method means that we're calculating the slope using this first equation shown here and calculating the Y intercept with the second equation. So first we will calculate the sample averages for X and Y. And then we will calculate the numerator and the denominator separately. And then finally find that quotation to give us our slope and we can do this in excel. So first step is to find the means we can use the average function for that and these are the two means that we get. Now let's calculate the numerator and the denominator. The numerator is the summation of each X. I subtracting the mean for the excess which is 87.4, which we just calculated times each of the y eyes minus the mean for why? Which is 6.64 And we want to do that for each eye and then we want to sum them. And then for the denominator, the denominator is the sum of each X. I minus the average of the excess, which is 87.4 and squared. So we do this for each eye and then we sum them. And so that's the numerator, this is the denominator. Our slope can be calculated by taking the numerator and dividing it by the denominator and we get a slope of about minus 0.0 to six. So that gives us piece of one is about minus zero point 0263 And from that we can calculate the intercept the wine bar was 6.64 and expire was 87.4. And this comes out to about 8.941 So that was part C. And we should finish writing the actual equation. So it's written like this. So plugging in our valley's, we have 8.941 minus 0.263 times X. Now for part D. We are asked to interpret the slope of the regression equation so that's minus 0.263 So our units are thousands of dollars and thousands of miles. So what it suggests is that for every 1000 mile increase on the car's odometer the price reduces by 0.263 thousands of dollars or $26.3. We can write that like that. And then for the were asked to predict the price of the car with 100,000 miles on it so we can use our regression equation to do this. So that's 100 1000 miles. Our units are in thousands already. And this comes out to about 6.3 which is $6300.

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