WHAT technology was used to answer these questions? What is the STEP-by-STEP gui

Question

WHAT technology was used to answer these questions? What is the STEP-by-STEP guide to using that particular technology?

The production of wine is a multibillion-dollar worldwide industry. In an attempt to develop a model of wine quality as

judged by wine experts, data was collected from red wine variants. A sample of 20 wines is provided in the table.

Develop a multiple linear regression model to predict wine quality, measured on a scale from 0 (very bad) to

10 (excellent) based on alcohol content (%) and the amount of chlorides.

QUESTION#1:> The wine quality prediction for a wine that has 8% alcohol and 0.10 chlorides is 2.410 units.Construct a 95% confidence

interval estimate for the mean quality rating for wines that have 8% alcohol and 0.10 chlorides.

(Use technology to solve this problem.)

ANSWER:> The 95% confidence interval estimate of the mean quality rating for wines that have 8% alcohol and 0.10 chlorides is

0.6 to 4.2, rounded to one decimal place.

QUESTION#2:> Construct a 95% prediction interval estimate for the quality rating for an INDIVIDUAL wine that has 8% alcohol and

0.10 chlorides.

(Use technology to solve this problem. Use the same method as in QUESTION#1 to find the prediction interval.)

ANSWER:> The 95% prediction interval estimate of the quality rating for an individual wine that has 8% alcohol and 0.10 chlorides is

1.5 to 6.3, rounded to one decimal place.

QUALITY Alcohol Content % Chlorides 0 6.9 .06 3 8.2 .06 0 7.6 .06 2 7.7 .08 1 7.8 .06 2 8.3 .07 5 7.9 .07 3 8.9 .08 4 9.6 .07 8 9.6 .07 5 11.1 .07 8 10.4 .07 7 11.6 .09 6 10.9 .09 7 12.1 .09 6 12.3 .08 10 12.7 .09 9 12.4 .1 8 13.1 .15 10 13.2 .17

Explanation / Answer

We can use any statistical software (technology ) to answer these questions. I am using R software to answer these questions. R commands used to solve the problems are given in italics.

I assume that the data is stored in txt file with name data.txt Load the data in a dataframe

df = read.table("data.txt", header = TRUE)

If the data is stored in csv file, load the data with the below command.

df = read.csv("data.csv", header = TRUE)

Develop a multiple linear regression model to predict wine quality.

Run the multiple regression in R.

model = lm(QUALITY ~ AlcoholContent + Chlorides, data = df)

QUESTION#1:> The wine quality prediction for a wine that has 8% alcohol and 0.10 chlorides is 2.410 units.Construct a 95% confidence interval estimate for the mean quality rating for wines that have 8% alcohol and 0.10 chlorides.

Store the given data in a dataframe.

newdata = data.frame(AlcoholContent = 8, Chlorides = 0.10)

95% confidence interval is given by the below command.

predict(model, newdata, interval="confidence")

The output of the command is,

fit lwr upr
2.401308 0.5764643 4.226151

So, 95% confidence interval of the mean quality rating for wines that have 8% alcohol and 0.10 chlorides is

(0.5764643 , 4.226151)

= (0.6, 4.2) (Rounded to one decimal place)

QUESTION#2:> Construct a 95% prediction interval estimate for the quality rating for an INDIVIDUAL wine that has 8% alcohol and 0.10 chlorides.

95% prediction interval is given by the below command.

predict(model, newdata, interval="predict")

The output of the command is,

fit lwr upr
2.401308 -1.460448 6.263063

So, 95% prediction interval of the mean quality rating for wines that have 8% alcohol and 0.10 chlorides is

(-1.460448 , 6.263063)

= (-1.5, 6.3) (Rounded to one decimal place)

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