4. A greenhouse plant is susceptible to a particular disease. We would like to d

Question

4. A greenhouse plant is susceptible to a particular disease. We would like to determine how the temperature of the greenhouse affects the prevalence of the disease. We monitor the percentage of diseased leaves occurring at different temperatures 78 4.3 Temperature, t °F 74. 76 80 % of diseased leaves, p | 12.3 | 10.2 | 8.0 6.1 2.3 Estimate the greenhouse temperature for which only 5% of leaves are diseased. Calculate an appropriate regression line of p vs. t and use it to find the required temperature

Explanation / Answer

calculation procedure for regression

mean of X = X / n = 75

mean of Y = Y / n = 7.2

(Xi - Mean)^2 = 70

(Yi - Mean)^2 = 69.28

(Xi-Mean)*(Yi-Mean) = -69.6

b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2

= -69.6 / 70

= -0.99429

bo = Y / n - b1 * X / n

bo = 7.2 - -0.99429*75 = 81.77143

value of regression equation is, Y = bo + b1 X

Y'=81.77143-0.99429* X

X Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 70 12.3 25 26.01 -25.5 72 10.2 9 9 -9 74 8 1 0.64 -0.8 76 6.1 1 1.21 -1.1 78 4.3 9 8.41 -8.7 80 2.3 25 24.01 -24.5

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