7. Suppose you are given 3 attributes of mobile phones - Brand, Price and Colour. 5 levels in brands, 4 levels in colour and 4 levels in price are considered. Given below is the output of dummy variable regression. (First level taken as reference in all attributes) (a part of the output is only shown) Coefficients Unstandardized Standardized Coefficients Coefficients Std. Beta Model B Error 1 (Constant) 1.280 1.151 brand B 0.480 0.164 0.455 brand C 0.301 0.121 0.247 brand D -0.024 0.256 -0.033 brand E 0.525 0.150 0.599 colour 2 0.022 0.116 0.022 colour 3 0.068 0.269 0.088 colour 4 0.042 0.096 0.043 price 2 -0.183 0.182 -0.161 price 3 -0.330 0.189 -0.259 price 4 0.093 0.156 0.070 a. Dependent Variable: Rating b. Predictors (constant) brand, colour, price From the given output: 7a. Find the percentage importance of brand, price and colour. 7b. Plot a part-worth diagram for the attribute - Brand. What is your observation? 6. X1, X2 & X3 are 3 variables that measure the loyalty of the customers towards a nationally reputed brand which is losing market share to international competitors. We have measured all three loyalty variables on a 10-point scale. The below table is a part of the output from SPSS (cluster analysis). Final Cluster Centres Cluster x3 x1 x2 Number of Cases in each Cluster 2 3 7 10 Cluster 16 66 55 10 10 1 45.000 2 32.000 3 33.000 Valid Missing 110.000 0.000 6a. what percentage of customers are most loyal to this brand? As a manager, what would be your strategy for each of these three groups of customers? 6b. How will you test the validity of these clusters? 5. While doing Factor Analysis using SPSS, you observed the KMO value as 0.50. What do you infer from this value? Explain how you can improve KMO value through reiteration? 4. Given below is the Component Matrix which is a part of the output from SPSS after doing Factor Analysis. Component Matrixa Age in years Level of education Years with current employer Component 1 2 0.790 0.213 0.067 0.884 0.863 -0.316 Household income in thousands 0.896 0.079 Debt to income ratio (x100) 0.056 -0.452 Extraction Method: Principal Component Analysis. a. 2 components extracted. Find the Eigenvalue corresponding to components 1 & 2? What percentage of the total variance is explained by components 1 & 2 together? (4 marks) 3. Explain Factor Score? Suggest a method that can be used instead of Factor score to create new data for further decision making? What is the main difference between these two methods in data analysis for business decisions? (5 marks) 2. Explain the methods used to measure multicollinearity? How would multi-collinearity affect your decision in business? (5 marks) 1. A study was conducted to analyse the effect of the age of a particular brand of car on their selling prices. 10 cars aged between 1 and 6 years old were randomly selected from the previous year's sales records. The SPSS output for linear regression is given below Model Summary Mode | R Square Adjusted R Square Std. Error of the Estimate 1 0.9289 1424.653 a. Predictors: (Constant), Y -- Age(in years) ANOVAa Model Sum of Squares df Mean Square F Sig. 240578912.62 118.533 Regression 240578912.621 1 1 Coefficientsa Standardized Unstandardized Coefficients Coefficients Model Sig. (Constant) Std. B Beta Error 29160.194 1143.289 9 25.505 5 0.000000 1 - X1 -- Age in -2790.291 256.289 -0.9679 years 10.887 3 0.000 a. Dependent Variable: Y -- Price($) Answer the following questions based on the given output 1a. Calculate and interpret R. 1b. Calculate and interpret R. 1c. Comment on the sample size used for this analysis with the help of the given output. 1d. Write down the regression equation. What is the expected decrease/increase in the sale price of a car (in dollars) when its age increases by 1 year? 1e. At 5% significance level do the data provide enough evidence to conclude that age is a useful predictor of the sale price of the car? Write down the hypotheses and derive the conclusion