14. -T.18 points WaneFMAC7 10.4.501.XP My Notes The following chart shows the to
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14. -T.18 points WaneFMAC7 10.4.501.XP My Notes The following chart shows the total annual support for the arts in a country by federal, state, and local government in 1995-2003 as a function of time in years (t 0 represents 1995) together with the regression line. (Assume a1.45, b 2.35, and c3.25.) Government funding for the Arts 0 1995 2003 Year (f) (a) Over the period [o, 4] the average rate of change of government funding for the arts was O less than the rate predicted by the regression line. O greater than the rate predicted by the regression line O approximately equal to the rate predicted by the regression line (b) Over the period [4, 8] the average rate of change of government funding for the arts was less than the rate predicted by the regression line. O greater than the rate predicted by the regression line O approximately equal to the rate predicted by the regression line (c) Over the period [3, 6] the average rate of change of government funding for the arts was less than the rate predicted by the regression line. O greater than the rate predicted by the regression line O approximately equal to the rate predicted by the regression lineExplanation / Answer
The co-ordinates of 0 are: (0,2.35) and the co-ordinates of 4 are: (4, 2.8 ) ( since the funding at 4 is 2.35 + (3.25-2.35)/2).
Average rate of change in governement funding in the period [0,4] = (y2-y1) / ( x2-x1)= 2.8-2.35/ ( 4-0) = 0.1125
Rate of change predicated by the regression line is: y2-y1 / (x2-x1) which is less than above since y2-y1 is less although the denominator is same.
This is equivalent to drawing a line joining the y-cordinates of 0 and 4. This line is above the regression line. Hence the answer is: greater than that predicated by the regression line.
b. Over the period [4,8],
Cordinates of 4: (4, 2.8 ) and co-ordinates of 8 are: (8, 1.9) ( since the funding at 8 is 1.45+0.9/2 = 1.45+0.45 = 1.9)
average rate of change : (1.9-2.8)/ (8-4 ) = -0.225, where as that predicated by the regression line if +ve. Hence the answer is : less than the rate predicted by the regression line.
C. Over the period [3,6]
Co-ordinates of 3 are: 3,2.35 and co-ordinates of 6 are: 6, 3.7
average rate of change ?: (3.7 - 2.35) / (6-3 ) = 0.45
THis is higher / greater than that predicted by the regression line.
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