3. We have data from an experiment below: 32 76 82 81 43 50 55 43 68 47 72 52 35

Question

3. We have data from an experiment below: 32 76 82 81 43 50 55 43 68 47 72 52 35 60 75 74 (a) The LSR equation for this set of data is = 54.027 0.11x. Find the correlation r and the coefficient of determination R2. Show your work. Analysis of Variance MS F-Value P-Value 0.734 Source Regression1 Error Total DF 31.41 31.41 0.13 6 1482.46 247.08 7 1513.88 Coefficients Coef SE Coef T-Value P-Value 0.027 0.734 Term Con tant 54.0 0.110 18.7 0.308 2.90 0.36 (b) The Minitab output for this experiment is given above. Based on the output, what is the interpretation of the ANOVA test? (c) Based on the output above, compute the 95% confidence interval for and give the interpretation of this CI. (Note that "x" is the predictor variable) (d) Draw a plot of the data. Do you see a relationship between x and y? Explain how the plot confirms the conclusions in each of the three previous parts (a), (b), and (c)

Explanation / Answer

1)R output is

> x=c(32,82,43,55,68,72,35,75)
> y=c(76,81,50,43,47,52,60,74)
> cor(x,y)
[1] 0.1440444

Therotically:

corr(x,y) = cov(x,y)/sqrt(var(x) * var(y))

= 40.82143/sqrt( 371.3571* 216.2679)

=  0.1440444

Coefficint of determenation : R2 = SSR/SST

= 31.41/1482.46

= 0.02075,

b) Anova Test:

Here p value is 0.734 so we rejectH0 . Regression coefficient not significant.

Therefore Regression line not Good fit.

d)

R output

plot(x,y)

from graph we observe that there is quadratic relationship betwean X and y

A

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