Using your calculator O computer software, scatterplot the data points Sketch the graph below. Does the relationship look linear? Find the least squares regression line. Write the model below and sketch the line on your graph in #4. What is the correlation coefficient? What does it tell you about the relationship between the gas mileage and average annual fuel cost? Do you think the variables have cause and effect relationship? Why?
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Scatterplot the data points: To do this, we need the data points. Please provide the data points for gas mileage and average annual fuel cost. Show more…
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Consider the following table of data. $$\begin{array}{|c|ccccc}{x} & {0} & {1} & {2} & {3} & {4} \\ {y} & {4} & {1} & {0} & {1} & {4}\end{array}$$ (a) Calculate the least squares line and the correlation coefficient. (b) Sketch a graph of the data. (c) Comparing your answers to parts (a) and (b), does a correlation coefficient of 0 mean that there is no relationship between the $x$ - and $y-$ values? Would some curve other than a line fit the data better? Explain.
Linear Functions
The Least Squares Line
Use the sample data to construct a scatterplot. Use the first variable for the $x$ -axis. Based on the scatierplot, what do you conclude about a linear correlation? The table lists weights (pounds) and highway fuel consumption amounts (mpg) for a Hyundai Elantra, Nissan Altima, VW Passar, Buick Luceme, Mercury Grand Marquis, Honda Civic, and Honda Accord. $$\begin{array}{|c|c|c|c|c|c|c|c|} \hline \text { Weight (lb) } & 2895 & 3215 & 3465 & 4095 & 4180 & 2740 & 3270 \\ \hline \text { Highway (mpg) } & 33 & 31 & 29 & 25 & 24 & 36 & 30 \\ \hline \end{array}$$
Exploring Data with Tables and Graphs
Scatterplots, Correlation, and Regression
Suppose the following scatterplot shows data relating the weight of a car (in pounds), x, and the gas mileage for that car (in miles per gallon), y, for a randomly selected sample of 9 cars. The best fit line/regression line has the equation ŷ = -0.021x + 96.51. a. Do you expect the correlation between the car weight and the gas mileage to be closer to 1, closer to 0, or closer to -1? Briefly explain how you know which one. b. Explain the meaning of the slope of the regression line in terms of the car weight and the gas mileage. (What does the number you have for slope tell us about how these variables change?) c. What does the model predict for the gas mileage if the car weighs 3500 pounds? Include units in your answer. d. In the sample, the actual gas mileage for a car of weight 2800 pounds was 35 miles per gallon. Find the residual for that car. Include units in your answer.
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