An article gave the following data on y = number of employees in fiscal year 2007–2008 and x = total size of parks (in acres) for the 20 state park districts in a state. Number of Employees, y Total Park Size, x 95 39,334 95 324 102 17,315 69 8,244 67 620,231 77 43,501 81 8,625 116 31,572 51 14,276 36 21,095 96 103,289 71 130,023 76 16,068 112 3,286 43 24,089 87 6,309 131 14,502 138 62,595 80 23,666 52 35,832 (a) Construct a scatterplot of the data. A scatterplot has 20 points. The horizontal axis is labeled "x" and ranges from 0 to 700,000.The vertical axis is labeled "y" and ranges from 0 to 150.The points are scattered mostly between approximately 0 and 150,000 on the horizontal axis and between approximately 35 and 140 on the vertical axis. One point is located at approximately (625,000, 65). A scatterplot has 20 points. The horizontal axis is labeled "x" and ranges from 0 to 700,000.The vertical axis is labeled "y" and ranges from 0 to 150.The points are scattered mostly between approximately 500,000 and 625,000 on the horizontal axis and between approximately 10 and 110 on the vertical axis. One point is located at approximately (0, 85). A scatterplot has 20 points. The horizontal axis is labeled "x" and ranges from 0 to 700,000.The vertical axis is labeled "y" and ranges from 0 to 150.The points are scattered mostly between approximately 500,000 and 625,000 on the horizontal axis and between approximately 35 and 140 on the vertical axis. One point is located at approximately (0, 65). A scatterplot has 20 points. The horizontal axis is labeled "x" and ranges from 0 to 700,000.The vertical axis is labeled "y" and ranges from 0 to 150.The points are scattered mostly between approximately 0 and 150,000 on the horizontal axis and between approximately 10 and 110 on the vertical axis. One point is located at approximately (625,000, 85). (b) Find the equation of the least-squares line. (Round your answers to five decimal places.) ŷ = + x(c) Do you think the least-squares line gives accurate predictions? Explain. (Round your numeric answer to one decimal place.) Based on r2we can say that % of the variation in the number of employees can be attributable to the least-squares line. Since this is , it to trust the line to give reliable predictions. (d) Delete the observation with the largest x value from the data set and recalculate the equation of the least-squares line. (Round your answers to five decimal places.) ŷ = + xDoes this observation greatly affect the equation of the line? Yes, removal of the point does greatly affect the equation of the line, since it changes the slope from negative to positive. No, removal of the point does not greatly affect the equation of the line. Yes, removal of the point does greatly affect the equation of the line, since it changes the slope from positive to negative.
An article gave the following data on y = number of employees in fiscal year 2007–2008 and x = total size of parks (in acres) for the 20 state park districts in a state.
Number of Employees, y
Total Park Size, x
95
39,334
95
324
102
17,315
69
8,244
67
620,231
77
43,501
81
8,625
116
31,572
51
14,276
36
21,095
96
103,289
71
130,023
76
16,068
112
3,286
43
24,089
87
6,309
131
14,502
138
62,595
80
23,666
52
35,832
(a)
Construct a
A scatterplot has 20 points.
The horizontal axis is labeled "x" and
The vertical axis is labeled "y" and ranges from 0 to 150.
The points are scattered mostly between approximately 0 and 150,000 on the horizontal axis and between approximately 35 and 140 on the vertical axis. One point is located at approximately (625,000, 65).
A scatterplot has 20 points.
The horizontal axis is labeled "x" and ranges from 0 to 700,000.
The vertical axis is labeled "y" and ranges from 0 to 150.
The points are scattered mostly between approximately 500,000 and 625,000 on the horizontal axis and between approximately 10 and 110 on the vertical axis. One point is located at approximately (0, 85).
A scatterplot has 20 points.
The horizontal axis is labeled "x" and ranges from 0 to 700,000.
The vertical axis is labeled "y" and ranges from 0 to 150.
The points are scattered mostly between approximately 500,000 and 625,000 on the horizontal axis and between approximately 35 and 140 on the vertical axis. One point is located at approximately (0, 65).
A scatterplot has 20 points.
The horizontal axis is labeled "x" and ranges from 0 to 700,000.
The vertical axis is labeled "y" and ranges from 0 to 150.
The points are scattered mostly between approximately 0 and 150,000 on the horizontal axis and between approximately 10 and 110 on the vertical axis. One point is located at approximately (625,000, 85).
(b)
Find the equation of the least-squares line. (Round your answers to five decimal places.)
ŷ = +
x
(c)
Do you think the least-squares line gives accurate predictions? Explain. (Round your numeric answer to one decimal place.)
Based on
r2
we can say that % of the variation in the number of employees can be attributable to the least-squares line. Since this is , it to trust the line to give reliable predictions.
(d)
Delete the observation with the largest x value from the data set and recalculate the equation of the least-squares line. (Round your answers to five decimal places.)
ŷ = +
x
Does this observation greatly affect the equation of the line?
Yes, removal of the point does greatly affect the equation of the line, since it changes the slope from negative to positive.
No, removal of the point does not greatly affect the equation of the line.
Yes, removal of the point does greatly affect the equation of the line, since it changes the slope from positive to negative.
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