Question

Astringency is the quality in a wine that makes the wine drinker’s mouth feel slightly rough, dry, and puckery. An investigation was conducted to assess the relationshipbetween perceived astringency (?) and tannin concentration (?) using various analytic methods. The data is provided in the “wine” worksheet where ?=tannin concentration by protein precipitation and ?=perceived astringency as determined by a panel of tasters.

a)Produce a scatterplot of the data. Does it appear that a simple linear regression model will be an appropriate fit to the data?Explain.

b)Findthe equation of the simple linear regression model for this datawith R.

c)Graph the regression line on the scatterplot produced in (a).

d)What proportion of observed variation in perceived astringency is explained by the tannin concentration of the wine?

e)Calculate and interpret a 95% confidence interval for the slope of the regression line.

x	y
0.718	0.428
0.808	0.48
0.924	0.493
1	0.978
0.667	0.318
0.529	0.298
0.514	-0.224
0.559	0.198
0.766	0.326
0.47	-0.336
0.726	0.765
0.762	0.19
0.666	0.066
0.562	-0.221
0.378	-0.898
0.779	0.836
0.674	0.126
0.858	0.305
0.406	-0.577
0.927	0.779
0.311	-0.707
0.319	-0.61
0.518	-0.648
0.687	-0.145
0.907	1.007
0.638	-0.09
0.234	-1.132
0.781	0.538
0.326	-1.098
0.433	-0.581
0.319	-0.862
0.238	-0.551

Answer 1

(a)

Following is the scatter plot:

(b)

The regression equation is:

y' = -1.5846 + 2.5849x

(c)

(d)

The proportion of observed variation in perceived astringency is explained by the tannin concentration of the wine is equal to r-sqaure. That is required proportio is 0.8373.

(e)

The confidence interval of slope is

(2.160067, 3.009823)

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Following is the screen shot of R:

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Following is the output:

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