Question

* 12.2 The table below shows the mass (y) of potassium bromide that will dissolve in 100ml of water at various temperatures (2). Temperature x°C Mass y (g) 0 54 20 65 40 60 75 85 80 96 (a) Find the regression line for predicting the y from . (b) Find the correlation coefficient, and test it for significance. (c) Find 95% prediction limits for predicting y when x = 50°C.

Answer 1

X: y Temperature Mass (°C) grums). a - Regression equation is 1 - 54.2 + 05.x Based on p output coefficient r= Comelation 0.9988 To test Hots=0 Histo Test statistics p-value = is 0.0000 t = 90.07 20.05 - » Reject Conclusion : - Ho at L=0.05 Comlation coefficient is significant o for 95% n = 50°C , y = 80.2 prediction intervalis (78.91 81.49] e 78.91 L Mila 50 L 81.49.

Note: R software output for the same is attached below

vvvvv > x=c(0,20,40, 60, 80) y=C(54, 65, 75, 85, 96) > ### Part- a] > fit=lm (yox) > summary (fit) Call: lm (formula = y - x) Residuals: 5 -2.000e-01 4.000e-01 -2.026e-15 -4.000e-01 2.000e-01 Coefficients: Estimate Std. Error t value Pr(tl) (Intercept) 54.200000 0.282843 191.63 3.13e-07 *** 0.520000 0.005774 90.07 3.02e-06 *** Signif. codes: 01***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ''i Residual standard error: 0.3651 on 3 degrees of freedom Multiple R-squared: 0.9996, Adjusted R-squared: 0.9995 F-statistic: 8112 on 1 and 3 DF, p-value: 3.017e-06 > predict (fit,newdata-data.frame (x=50),interval="prediction", level=0.95) fit lwr pr 1 80.2 78.91383 81.48617 > cor (x,y) [1] 0.9998151