suppose you have n data points (1, y1). (r2, y2) .... (xas ya) and you wish to ht a line through the origin (y = ax) to these data using the method of least squares. derive equation al-6 (appendix al) for the slope of the line by writing the expression tor the vertical distance d, from the i th data point (x, y) to the ine, then writing the expression for o2dj, and inding by differentiation the value of a that minimizes this tunction.
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have worked with a random variable x that comes from a population that is
normally distributed with mean µ and variance σ2. We have seen that we can write x in terms
of µ and a random error component ε, that is, x = µ + ε. For the time being, we are going to
change our notation for our random variable from x to y. So, we now write y = µ+ε. We will now
find it useful to call the random variable y a dependent or response variable. Many times, the
response variable of interest may be related to the value(s) of one or more known or controllable
independent or predictor variables. Consider the following situations:
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