b) Write down assumed model, fit the model and provide the fitted equation. Call
ID: 3054310 • Letter: B
Question
b) Write down assumed model, fit the model and provide the fitted equation. Call: 1m(formula y acid. temp acid. conc water.tempsulf.conc + amt.bl., data rayon) Residuals: -14.8929 7.7179 0.0696 5.9581 19. 9946 Coefficients: Min 1Q Median 3Q Max (Intercept) -35. 2626 62.0105 0. 569 0. 57592 acid. temp acid. conc 20. 2292 10. 5045 1.926 0.06847. water.temp 0.7931 sulf.conc 25. 5833 42.0181 0.609 0. 54947 amt.bl. Estimate Std. Error t value Pr(>ItI) 0. 2101 3.548 0.00202 0.7003 1.132 0.27084 17.2083 21.0090 0.819 0.42239 0. 7454 Signif. codes: O0.001 **0. 010.05 0.11 Residual standard error: 10.29 on 20 degrees of freedom Multiple R-squared: 0.4822, Adjusted R-squared: 0.3527 F-statistic: 3.724 on 5 and 20 DF, p-value: 0.01518 c) Assess the significance of regression. Is regression significant? What does this tell you? d) Test if the regression coefficients are equal to zero or not at 5% level. e) Support your decision by constructing one-at-a-time confidence intervals for each regression parameter. What is the probability that all of the one-at-a-time confidence intervals simultaneously are correct?Explanation / Answer
b)
y^ = -35.2626 + 0.7454 * acid_temp +20.2292 acid_conc +0.7931 * water_temp +25.5833 sulf_conc +17.2083
c)
p-value = 0.01518 < 0.05
hence the regression is significant ar 5 % level of significance
d)
if p-value of regression coefficient is less than 0.05
then that variable is significant
here only acid_temp is significant and rest are not
e)
df = 20
t-critical = 2.086
confidence interval
= (point estimate - t * std. error , point estimate + t * std. error )
hence
for acid_temp
(0.7454 - 2.086 * 0.2101 , 0.7454 + 2.086 * 0.2101)
= (0.3071314 , 1.1836686)
if 0 is not present in confidence interval , it means that the variable is significant
hence acid_temp is significant
similarly you can do for other variables
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