Question

6.5. Brand preference. In a small-scale experimental study of the relation between degree of brand liking (Y) and moisture content (Xi) and sweetness (X2) of the product, the following results were obtained from the experiment based on a completely randomized design (data are coded): 2 4 4 73 3 4 61 15 10 94 16 10 100 Xi1: 4 10 4 95 64 a. Obtain the scatter plot matrix and the correlation matrix. What information do these diag- b. Fit regression model (6.1) to the data. State the estimated regression function. How is lr c. Obtain the residuals and prepare a box plot of the residuals. What information does this plot d. Plot the residuals against f, X, X2, and X,X2 on separate graphs. Also prepare a normal nostic aids provide here? interpreted here? provide? probability plot. Interpret the plots and summarize your findings.

Answer 1

Answer:

a)

On the basis of given visible data got the scatter matrix and correlation matrix as follows:

Moisture content vs Brand liking Moisture content vs Sweatness 4.5 3.5 2.5 a 40 15 20 0.5 10 12 10 12 Moisture content Moisture content Moisture content vs Brand liking 120 100 40 20 0 05 15225 Sweatness 5 45

moisture sweatnes king content Brand 7 moisture content1.0000000 0.3333333 0.9660646 sweatness 0.3333333 1.0000000 0.5201886 Brand liking 0.9660646 0.5201886 1.0000000

We can say that both moisture content and sweatness are not highly correlated i.e. these varaibles are indepedent.

Dependent variable Brand liking is highly positively correlated with Moisture content(0.96) and with sweatness correlation is 0.52 which is also showing positive correlation with Brand liking.

b)

After fitting the simple linear regression model to the data in R we got results:

Intercept B₀=38.0

> coefficients(Im(trains Brand liking trains moisture content +trainSsweatness, data-train)) (Intercept) train$ moisture content train$sweatness 3. 500000 38.000000 4.666667

coefficient of moisture content B₁=4.67

coefficient of sweatness B₂=3.5

both coefficients are positive which shows when increases the one variable by one unit brand liking will increase by coefficients time of that variable.

c)

residuals we got from the model are:

Box plot :

> residuals(lm(trains Brand liking -trains moisture content +trainssweatness, data-train)) 2 0. 3333333 2. 3333333-2.6666667 -3.6666667 2.3333333 1. 3333333

CN CN

d)

graphs are as follows:

Moisture content 10 12 -1 -2 -4

Fig.1 Residuals vs moisture content

Sweatness 0.5 1.5 2.5 3.5 -1 -2 -4

Predicted brand liking 20 40 60 80 100 120 -2 -3

X1*X2 5 10 15 20 25 3035 4045 -1 -2 -3 -4