A state's park system statistical report for the 2014/2015 fiscal year gave the accompanying data on x = amount of money collected in user fees (in thousands of dollars) and y = operating cost (in thousands of dollars) for nine state parks in a certain district.
User Fees (thousands of dollars) Operating Costs (thousands of dollars)
17 101
74 363
811 3,618
380 1,391
33 239
427 760
500 1,034
734 2,227
760 1,604
(a) Construct a scatterplot of the data.
A scatterplot has 9 points. The horizontal axis is labeled "x" and ranges from approximately 0 to 900. The vertical axis is labeled "y" and ranges from 0 to 4,000. The points are plotted from left to right in an upward, diagonal direction starting from the lower left corner of the diagram. The points are somewhat scattered, becoming more scattered from left to right, and are between the approximate horizontal axis values of 10 and 820 and between the approximate vertical axis values of 100 and 3,700.
(b) Find the equation of the least squares regression line (the equation of the best fit line). Hint: use Excel to perform calculations with larger datasets. (Round your answers to three decimal places.)
Å· = a + bx
(c) Is the slope of the least squares regression line positive or negative? Is this consistent with your description in part (a)?
The slope is negative, which is consistent with the description in part (a).
(d) Based on the scatterplot, do you think that the correlation coefficient for this data set would be less than 0.5 or greater than 0.5? Explain.
The correlation coefficient would be less than 0.5, because the relationship appears weak.