Answer Happy

A retail outlet wants to distinguish between the two brands (labelled brand 1 and brand 2) of a product sold by using income (xl) and household size (x2) as classification variables. The data that were collected are shown below. x2 brand 1 4 1 1 1 1 x1 168 214 173 184 232 211 145 x2 3 2 4 1 1 1 1 brand 2 2 2 2 2 2 2 2 2 2 3 4 5 2 6 7 2 5 4 x1 173 154 143 145 174 167 139 124 153 133 1 189 7 1 1 1 2 2 1 178 193 6 1 1 4 The sample mean vectors for brands 1 and 2 and the pooled estimate of the variance- covariance matrix are -102.25) 4.8 - 102.25 22.05 *: = (12.5%). 8 = (1505) and Spur = (4164,3 8z 712 = (4) 2.1 By making use of the above information, calculate the equation of the linear discriminant function that can be used to classify observations as brand 1 or brand 2. 1 2.2 The first 2 observations under brand 1 and the first observation under brand 2 in the above table are x1 x2 3 168 214 173 2 4 By making use of your linear discriminant function in part 1, classify each of these 3 cases as brand 1 or brand 2 observations. Show all calculations. (10) 2.3 The following table of classification counts according to brands was obtained from an R program. actual/classified 1 2 2 2 1 8 21 21 8 2.3.1 What percentage of cases was correctly classified? ( (1) 2.3.2 What percentage of cases that should have been brand 2 was incorrectly classified as brand 1? (1)