Applied Business Forecasting and Planning. Simple Linear Regression. Simple Regression.
Simple Linear Regression
1. Regard Y as a random variable.
2. For each X, take f (x) to be the expected value (i.e., mean value) of y.
3. Given that E (Y) denotes the expected value of Y, call the equation
the regression function.
we can summarize the relationship by drawing a straight line on the plot.
SALES = 0 + 1 AREA +
where is a random variable with a normal distribution with mean 0 and standard deviation .
The residual plot to right shows a scatter of the points with no individual observations or systematic change as x increases.Residual plots
The points in this residual plot have a curve pattern, so a straight line fits poorlyResidual plots
The points in this plot show more spread for larger values of the explanatory variable x, so prediction will be less accurate when x is large.Residual plots
Reject H0 if
Since t =4.5 > 2.306 then we reject H0.
There is a linear association between advertising expenditure and weekly sales.
H0: 1 = 0, Ha: 1 > 0
SSE = 36124.76
SST = 128552.5
MSR = 92427.74
MSE = 4515.6
1 0 is equivalent algebraically to the two sided t-test.
b1 = 0 so that , SSE=SST and R2 = 0.