How to interprete the minitab output of a regression analysis

# Step vii let us estimate the value of y and interpret

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Step VII: Let us estimate the value of y and interpret it Say for x = 14 we find and interval for the average value of y y-hat = 123 - 5.57 * 14 = 45.02 that is we expect that on the average the expected value of weight on the 14 th day approx 45 grams. 98% confidence interval: 45.02 ± t * .8441 = 45.02± 2.326*.8441= (43.0565, 46.9635)

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We are 98% confidant that that on the 14 th day the weight of the soap on the average lies between 43 grams and 47 grams approx. 98% prediction interval: 45.02± 2.326* 3.1163 = (41.9036, 48.1363) We are 98% confidant that on the 14 th day the predicted value of the weight of the soap lies between 42 grams and 48 grams approx. Day 25 20 15 10 5 0 0 0 0 0 0 0 0 0 S 2.94921 R-Sq 99.5% R-Sq(adj) 99.5% Regression 95% CI 95% PI Fitted Line Plot Weight =  123.1 - 5.575 Day (optional)For those who want to improve upon the model Quadratic fitting: compare the s-value and Rsq adj value with last model.
Day 25 20 15 10 5 0 140 120 100 80 60 40 20 0 S 1.95599 R-Sq 99.8% R-Sq(adj) 99.8% Regression 95% CI 95% PI Fitted Line Plot Weight =  127.3 - 6.744 Day + 0.05063 Day* * 2 Validation of assumptions in quadratic fitting: Residual Percent 5.0 2.5 0.0 -2.5 -5.0 99 90 50 10 1 Fitted Value Residual 120 90 60 30 0 2 0 -2 -4 Residual Frequency 3 2 1 0 -1 -2 -3 -4 4 3 2 1 0 Observation Order Residual 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 2 0 -2 -4 Normal Probabilit y Plot  of t he Residuals Residuals Versus t he Fit t ed Values Hist ogram of t he Residuals Residuals Versus t he Order of t he Dat a Residual Plots for Weight
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