An experiment was carried out to investigate the relationship between the weight

Question

An experiment was carried out to investigate the relationship between the weight of a jute plant and the weight of jute fiber that can be extracted from it. The data are given in the following table:

TI-84 calculator

a = 0.1565

b = 0.0768

r = 0.9576

y = 0.0768x + 0.1565

Residuals:

Coefficients:

                Estimate Std. Error t value Pr(>|t|)  

(Intercept)        5.302      5.892   0.900 0.41905  

Book2$`w-fiber`   11.944      1.798   6.645 0.00266 **

Residual standard error: 5.647 on 4 degrees of freedom

Multiple R-squared: 0.9169, Adjusted R-squared: 0.8962

F-statistic: 44.15 on 1 and 4 DF, p-value: 0.002663

My question is how do I Evaluate a 95% confidence interval for the slope, b1 of the true regression line?

Explanation / Answer

Answer to the question is as follows:

To this just calculate the following:

Mean +/- Z*SE

We pick the values from the table at the end of the question. Please cross check the below values to understand how I have calculated b1' confidence interval:

= (beta coefficient of slope) +/- 1.96* (SE of slope)
= 11.944 +/- 1.96*1.798
= 8.41992 to 15.4681

Answer : the 95% Ci is given by 8.41992 to 15.4681

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