For questions 7-9, suppose that we have two quantitative variables X and Y. Seve
ID: 3170791 • Letter: F
Question
For questions 7-9, suppose that we have two quantitative variables X and Y. Seven observations are given below in the following table. The goal is to predict the value of Y, given a value of X One way of fitting a regression line is to just use the mean of Y for each value of X. That is, we fit Y = Y, where Y is the sample mean of Y. The scatterplot shows this model as the green line depicted below. Find the sample mean of the response variable, that is, find y. Calculate the quantity SST = sigma(y_i - y)^2. This quantity is called the total sums of squares. It gives us an idea of the total amount of variation in the response variable Y. Find the standard error of the estimate s_e for this equation and interpret what it means.Explanation / Answer
a) from abovre sample eman =690.26
b)SST =48398.286
c) from above standard error of the estimate se =(94328.293/(7-2))1/2=137.35
this represent the deviation in value of response variable because of unknown reasons except those of indpendent variable.
s. No x Y (X-Xbar)^2 (Y-Ybar)^2 (X-Xbar)(Y-Ybar) Yi'=b0+x*b1 (Y-Yi')^2 1 244 456 1836.7347 54889.796 10040.816 485.4628 868.0574 2 260 614 721.3061 5819.510 2048.816 561.9300 2711.2817 3 264 567 522.4490 15199.367 2817.959 581.0468 197.3136 4 364 943 5951.0204 63864.510 19495.102 1058.9669 13448.3297 5 278 628 78.4490 3879.510 551.673 647.9556 398.2279 6 318 1088 969.8776 158176.653 12385.959 839.1237 61939.4186 7 280 536 47.0204 23804.082 1057.959 657.5141 14765.6644 total(T) 2008.0000 4832.0000 10126.8571 325633.4286 48398.286 94328.29342