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Two-variable data: Models and scatterplots SAT question

Math · Problem-Solving and Data Analysis · Easy · Answer it here, explanation included.

The figure presents a scatterplot titled “Temperature and Elevation.” The horizontal axis is labeled “Elevation, in feet,” and the numbers 6,000 through 9,000, in increments of 500, are indicated. The vertical axis is labeled “Temperature, in degrees Fahrenheit,” and the integers 37 through 45 are indicated. There are 8 data points. The data points begin a little below, and to the right of the top of the vertical axis, then trend downward and to the right. A line of best fit is drawn. The data represented by the 8 data points are as follows. Note that all values are approximate. Point 1. 6,350 feet, 42 point 9 degrees Fahrenheit. Point 2. 6,750 feet, 43 point 8 degrees Fahrenheit. Point 3. 6,750 feet, 42 degrees Fahrenheit. Point 4. 7,500 feet, 42 point 2 degrees Fahrenheit. Point 5. 8,000 feet, 40 point 5 degrees Fahrenheit. Point 6. 8,000 feet, 40 degrees Fahrenheit. Point 7. 8,800 feet, 38 point 6 degrees Fahrenheit. Point 8. 8,800 feet, 37 point 6 degrees Fahrenheit. The line of best fit passes through the data point representing 7,500 feet comma 41 point 1 degrees Fahrenheit, and the data point representing 8,500 feet comma 39 degrees Fahrenheit

The scatterplot above shows the high temperature on a certain day and the elevation of 8 different locations in the Lake Tahoe Basin. A line of best fit for the data is also shown. What temperature is predicted by the line of best fit for a location in the Lake Tahoe Basin with an elevation of 8,500 feet?

ExplanationShow

Choice B is correct. The line of best fit passes through the point with coordinates 8,500 comma 39. Therefore, the line of best fit predicts a temperature of 39°F for a location in Lake Tahoe Basin with an elevation of 8,500 feet.

Choice A is incorrect. This is the lowest temperature listed on the scatterplot, and the line of best fit never crosses this value for any of the elevations shown. Choice C is incorrect. According to the line of best fit, the temperature of 41°F is predicted for an elevation of slightly greater than 7,500 feet, not an elevation of 8,500 feet. Choice D is incorrect. According to the line of best fit, the temperature of 43°F is predicted for an elevation of roughly 6,700 feet, not an elevation of 8,500 feet.

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