Question

Question 1 (18 points) The article 'The Selection of Yeast Strains for the Production of Premium Quality South African Brandy Base Products' (C. Steger and M. Lambrechts, Journal of Industrial Mi- croobiology and Biotechnology, 2000:431-440) presents detailed information on the volatile compound composition of base wines made from each of 16 selected yeast strains. Below are the concentrations of total esters and total volatile acids (in mg/L) for each of the wines. ## Warning: package 'knitr' was built under R version 3.6.1 Esters Acids 180.60 239.88 224.08 308.72 159.99 227.90 198.08 265.84 214.92 291.71 220.15 297.87 171.30 234.42 150.05 207.29 206.68 281.01 214.98 292.76 193.74 262.31 211.87 275.18 163.04 232.02 245.70326.29 174.97 257.47 249.25 332.00 a) (6 points) Construct a scatterplot of total acid vs. total ester. Does a linear model seem appropriate to describe the relationship between these variables? Why or why not? b) (3 points) Compute the least squares line which predicts total volatile acid. Write the fitted line using proper notation. c) (9 points) You are interested in deciding whether or not there is evidence of a linear relationship between these variables. The null hypothesis is H, :B1 = 0. Report the test statistic, null distribution, and p-value for this test.

I do not need help with part a.

Answer 1

b).

The EXCEL output for the linear regression is given below.

SUMMARY OUTPUT Regression Statistics Multiple R 0.984786549 R Square 0.969804547 Adjusted R Square 0.967647729 Standard Error 6.562888259 Observations 16 ANOVA Significance F df SS MS F Regression 1 19366.92741 19366.92741 449.6459695 4.85886E-12 Residual 43.0715023 14 603.0010322 Total 15 19969.92844 Coefficients Standard Error P-value t Stat Lower 95% Upper 95% Intercept 32.22988198 11.3693565 2.834802654 0.013240814 7.845037511 56.61472646 Esters 1.200538431 0.0566162 21.20485722 4.85886E-12 1.07910876 1.321968103

The fitted regression equation is,

Predicted(Acids) = 32.23 + 1.2 (Esters).

The test statistic for the regression coefficient is 21.205 and the corrosponding p-value is approximately zero.

Therefore, the predictor Esters is significant in the model and effecitve in predicting Acids.

The R-squared value for the model is 0.9698. it indicates that the model explaining approximately 97% of the variability in Acids which is very significant.