Question

Temperature Turbidity [FAU] 125 118 103 105 26 90 22.9 24.0 22.9 23.0 20.5 26.2 25.8 26.1 26.9 22.8 27.0 26.1 26.2 26.6 100 105 267 286 235 265 A. Determine the p-value for model significance by finding the value of a where the confidence interval of the slope is zero

Answer 1

Using Minitab software (Stat -> Regression -> Regression -> Fit Regression Model), we get the following output :

Minitab Untitled File Edit Data Calc Stat Graph Editor Tools Window Help Assistant Session Regression Analysis: Turbidity versus Temperature Model Summary S R-sqR-sq (adj) R-sq(pred) 35 . 70% 67.6777 40.64% 23.11% Coefficients Coef SE Coef T-Value P-Value VIF -511 Term -2.24 2.87 Constant 228 0.045 0.014 1.00 Temperature 26.31 9.18 Regression Equation Turbidity -511 26.31 Temperaturel C1 C2 C3 C4 CS C6 Temperature Turbidity 125 22.9 24.0 118 22.9 103 105 23.0 4 20.5 26 26.2 90 25.8 26.1 100 105 26.9 22.8 10 267 27.0 Pro....O Current Worksheet: Worksheet 1 Type here to search

Here,

The regression equation is : Turbidity = -511 + 26.31 Temperature

For testing the significance of the slope,

estimated slope

31 26.31

standard error of slope

SE(B) 9.18

The value of test statistic

t=53(3) = 287 SE B1)

associated degrees of freedom =n -2 = 14 - 2 = 12

P-value =

Pltn-2| > tobs) = P(hol > 2.87) 0.014

Since p-value < 0.05, so at 5% level of significance we can conclude that the slope is statistically significant.