(b) Now consider a transformation ylog y. We are using common logarithms of base
ID: 3368342 • Letter: #
Question
(b) Now consider a transformation ylog y. We are using common logarithms of base 10 (however, natural logarithms of base e would work just as well). 0.477 1.079 1.342 1.708 2.161 Look at the Excel graph of the scatter diagram of the (x, y) data pairs and compare this diagram with the diagram in part (a). Which graph appears to better fit a straight line? 25 2.0 1.5 1.0 D.5 Part (b) Model with (x y) Data Pairs The two diagrams are different. The transformed data do not fit a straight line better The two diagrams are the same The two diagrams are different. Both fit a straight line just as well. The two diagrams are different. The transformed data fit a straight line better (c) use a calculator with regression keys to find the linear regression equation for the (x, y) data pairs with sample correlation coefficient r = 0.882. (Round your answers to three decimal places.) (d) Use a calculator with regression keys to find the linear regression equation for the (x, y') data pairs with sample correlation coefficient r = 0.993. The sample correlation coefficient r = 0.882 for the (x, y) pairs is not bad. But the sample correlation coefficient r = 0.993 for the (x, y') pairs is a lot better! (Round your answers to three decimal places.) (e) The exponential growth model is y-gly. Let us use the results of part (d) to estimate ? and ? for this strain of laboratory bacteria. The equation y' = a + bx is the same as log y = a + bx If we raise both sides of this equation to the power 10 and use some college algebra, we get y = 10a(10b)". Thus, ? 10a and ? 1o5. Use these results to approximate ? and ? and write the exponential growth equation for our strain of bacteria. (Round your answers to three decimal places.)Explanation / Answer
(b) The two diagrams are different. The transformed data fit a straight line better.
(c) We need to find this equation : y = a + bx
b = Cov(x,y) / Var(x)
Cov(x,y) = E(xy) - E(x) * E(y)
Var(x) = E(x2) - ( E(x) )2
So, b = 32.28
a = E(y) - b * E(x) = - 50.2634
So , y = - 50.2634 + 32.28 x
(d) Similarly as part (c)
b = Cov(x,y') / Var(x) = 0.3997
a = E(y) - b * E(x) = 0.1543
So , y' = 0.1543 + 0.3997 x
(e)
Alpha = 10a = 100.1543 = 1.4266
Beta = 10b = 100.3997 = 2.51
So , y = 1.4266* 2.51x
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