8. (From Stapleton, 1995.) Suppose we have an ordinary household scale such as might be used...
8. (From Stapleton, 1995.) Suppose we have an ordinary household scale such as might be used in a kitchen. When an object is placed on the scale, the reading is a combination of the true weight plus a random error. You have two coins of unknown weights ß, and 62. To estimate the weights of the coins, you take four observations: . Put coin 1 on the scale and observe y e Put coin 2 on the scale and observe y2 . Put both coins on the scale and observe y's, - Put both coins on the scale again and observe Suppose the random errors are independent and identically distributed (a) Write a linear model in matrix form and find the least-squares estimates of the coins using the usual formula (X(X)Xy (b) Explain in words why at least parts of the estimates of the coins make sense. (The denominator 5 may not be intuitive.)