The past 20 monthly sales figures for a new type of watch sold at Lambert's Discount Stores are given in Table 16.6.
a. Plot the watch sales values versus time and discuss why the plot indicates that the model
yt = β0 + β1t + ε1
might appropriately describe these values.
b. The least squares point estimates of β0 and β1 can be calculated to be b0 = 290.089474 and b1 = 8.667669. Use b0 and b1 to show that a point forecast of watch sales in period 21 is ŷ 21 = 472.1 (see the Excel output in Table 16.6). Use the formulas of simple linear regression analysis or a computer software package to show that a 95 percent prediction interval for watch sales in period 21 is [421.5, 522.7].