(a) Find a regression relating steam usage to temperature. (b) Test for significance of regression using a=0.05. (c) Find a 99% confidence interval for B1
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Answer: Regression analysis is concerned with the study of the dependence of one variable, the dependent variable, on one or more other variables, the explanatory variables.
The two - variable linear model, or simple regression analysis, is used for testing hypothesis about the relationship between a dependent variable Y and an independent or explanatory variable X and for prediction. Simple linear regression analysis usually begins by plotting the set of XY values on a scatter diagram and determining by inspection if there exists an approximate linear relationship. It's model is,
Where = intercept or constant and = Slope or coefficient of regressor, e = Error term
In above example Y = The number of pounds of steam usage
X = The average monthly temperature
Fit the regression model Y to X is
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