the gas milage of an automobile first incrases and then decreases as the speed increases. find the seven standardized values for each variable
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Let them be: (x1, y1), (x2, y2), ..., (x7, y7) where x = speed and y = gas mileage. Show more…
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The gas mileage of an automobile first increases and then decreases as the speed increases. Suppose that this relationship is very regular, as shown by the data in the table on speed (miles per hour) and mileage (miles per gallon): Speed Mileage 30 24 40 28 50 30 60 28 70 24 To access the complete data set, click the link for your preferred software format: Excel Minitab JMP SPSS TI R Mac-TXT PC-TXT CSV CrunchIt! Make a scatterplot of mileage versus speed. You should notice that the correlation between speed and mileage is r = 0.
David N.
How does the fuel consumption of a car change as its speed increases? The table contains data for a 2013 Volkswagen Jetta Diesel. Speed is measured in miles per hour, and fuel consumption is measured in miles per gallon. Speed Fuel 20 49.0 30 67.9 40 66.5 50 59.0 60 50.4 70 44.8 80 39.1 Click to download the data in your preferred format. CSV Excel JMP Mac-Text Minitab14-18 Minitab18+ PC-Text R SPSS TI CrunchIt! Describe the form of the relationship. It is not linear. Explain why the form of the relationship makes sense. The relationship is curved — low at the two extremes, high toward the left, and steadily decreasing as the speed increases. This makes sense because most speed limits in the city are around the speed where the peak occurs in the graph. The relationship is curved — downwards overall, but with a pair of outliers. This makes sense because neither a perfect fit nor a straight line should be expected for such a complex machine. The relationship is curved — low at the two extremes, high toward the left, and steadily decreasing as the speed increases. This makes sense because engines are designed for specific speed, temperature, and rpm ranges. Driving out of these ranges goes against the fundamental design of the engine, leading to less efficient use of fuel. There is no particular form to the relationship. This makes sense because the fuel efficiency is better explained by other factors besides speed; for example, temperature, rpm, and wind speed.
Ivan K.
Gas mileage is tested for a car under different driving conditions. At lower speeds, the car is driven in stop and go traffic. At higher speeds, the car must overcome more wind resistance. The variable $x$ given in the table represents the speed (in mph) for a compact car, and $m(x)$ represents the gas mileage (in $\mathrm{mpg}$ ). $$\begin{array}{|c|c|c|c|c|c|} \hline \boldsymbol{x} & 25 & 30 & 35 & 40 & 45 \\ \hline \boldsymbol{m}(\boldsymbol{x}) & 22.7 & 25.1 & 27.9 & 30.8 & 31.9 \\ \hline \end{array}$$ $$\begin{array}{|c|c|c|c|c|} \hline \boldsymbol{x} & 50 & 55 & 60 & 65 \\ \hline \boldsymbol{m}(\boldsymbol{x}) & 30.9 & 28.4 & 24.2 & 21.9 \\ \hline \end{array}$$ a. Use regression to find a quadratic function to model the data. b. At what speed is the gas mileage the greatest? Round to the nearest mile per hour. c. What is the maximum gas mileage? Round to the nearest mile per gallon.
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