part b

• Regression analysis calculates an equation that provides values of Y

  for given values of X
• The Least Squares Method method uses calculus techniques

  to find the minimum of the sum of the squares of the vertical

  distances of each data point from the proposed line.
• When the measurements are plotted as points on a graph and seem to

  fall near the same line, the least squares method may be used to

  determine the best-fitting line
• The interpretation of b1 ( called regression coefficient or slope)

  is the expected change in Y for a one-unit change in X when the

  other covariates (when they exist) are held fixed.
• The interpretation of b0 (called intercept) is the Y value of the line

  when X equals zero. It defines the elevation of the line.
• The sum of all the squared residuals is known as the residual sum

  of squares (RSS) and essentially provides a measure of model-fit
• A poorly fitting model will deviate markedly from the data and will

  consequently have a relatively large RSS, whereas a good-fitting

  model will not deviate markedly from the data and will

  consequently have a relatively small RSS (a perfectly fitting model

  will have an RSS equal to zero, as there will be no deviation).
• It is convenient to divide RSS by the number of observations to

  get the average value i.e. the residual standard deviation. The

  smaller the residual standard deviation, the closer is the fit to the

  data.
• The summary measure of prediction error is called residual standard

  deviation (standard error)