Use the following information to answer problems 1 to 15 below: You have modifie

Question

Use the following information to answer problems 1 to 15 below: You have modified laetisaric acid to 3-hydroxy-acetyl-laetisarate and believe it could be used as an anti-fungal agent to control the growth of fungus on wet corn leaves. You grow the fungus Pythium sp. in 8 petri dishes containing fungal growth agar (PDA = potato dextrose agar) and various concentrations of your new anti-fungal agent. After 48 hours of growth in an incubator the diameters of all fungal colonies are measured with the following results: Some numbers to help you: sigma x = 140 sigma x^2 = 3,500 sigma y = 239.7 sigma y^2 = 7,353.97 sigma xy = 3,809.5 n = 8 Calculate b_1 Calculate b_0 Set up the ANOVA table for simple linear regression. Calculate the correlation coefficient (Pearson's r) Calculate the Coefficient of Determination AND give an EXACT interpretation in light of these data. Calculate the JOINT 95% confidence intervals for beta_1 and beta_0 Test to see if the y-intercept is zero or not. Use the usual five step procedure at alpha = 0.05 Test to see if the slope is zero or not. Use the usual five step procedure at alpha = 0.05 Calculate the 95% confidence interval for the population correlation coefficient. Since n is small, use z = 1.960 for your calculation. If a concentration of 22 mug/ml of 3-hydroxy-acetyl-laetisarate is used(x value), then calculate the expected fungal colony diameter (y value). For #10 above, calculate the 95% confidence interval for E[Y_h] Since y_h = y_h(new), calculate the 95% prediction interval for for y_h = y_h(new) for x = 22.0 mug/ml. Given that y_h = y_h(new) = 30.0 mm, calculate x_h = y_h(new) Calculate the 95% confidence interval for x_h = y_h(new) in #14 above For x_h = y_h(new) values of 12.5, 31.0 and 40.0, calculate the three simultaneous 95% confidence intervals for E[Y_h] using the Working-Hotelling method.

Explanation / Answer

Sol)

The Regression equation is a+bx

From Excel

From Above analysis

1)b1= -0.37

2) b0= 36.38

3)

4)

Correlation coefficient is 0.91

Hence we say that there is 91% Correlation between X and Y

5) Coefficient of determination is 0.82

Hence 82% of variation in y explained by x

Coefficients Standard Error t Stat P-value Intercept 36.38333 1.45794496 24.95522 2.73E-07 X -0.3669 0.069703101 -5.26382 0.001894

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