Given the following regression output, Predictor Coefficient SE Coefficient t p-value Constant 84.998 1.863 45.62 0.000 x1 2.391 1.200 1.99 0.051 x2 -0.409 0.172 -2.38 0.021 Analysis of Variance Source DF SS MS F p-value Regression 2 77.907 38.954 4.138 0.021 Residual Error 62 583.693 9.414 Total 64 661.600 answer the following questions: e-1. State the decision rule for each independent variable. Use the 0.05 significance level. (Round your answers to 3 decimal places. Negative values should be indicated by a minus sign.) e-2. Compute the value of the test statistic. (Round your answers to 2 decimal places. Negative values should be indicated by a minus sign.) e-3. Which variable would you consider eliminating?
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!
Given the following regression output,
| Predictor | Coefficient | SE Coefficient | t | p-value | ||||||||
| Constant | 84.998 | 1.863 | 45.62 | 0.000 | ||||||||
| x1 | 2.391 | 1.200 | 1.99 | 0.051 | ||||||||
| x2 | -0.409 | 0.172 | -2.38 | 0.021 | ||||||||
| Analysis of Variance | ||||||||||
| Source | DF | SS | MS | F | p-value | |||||
| Regression | 2 | 77.907 | 38.954 | 4.138 | 0.021 | |||||
| Residual Error | 62 | 583.693 | 9.414 | |||||||
| Total | 64 | 661.600 | ||||||||
answer the following questions:
-
e-1. State the decision rule for each independent variable. Use the 0.05 significance level. (Round your answers to 3 decimal places. Negative values should be indicated by a minus sign.)
-
e-2. Compute the value of the test statistic. (Round your answers to 2 decimal places. Negative values should be indicated by a minus sign.)
-
e-3. Which variable would you consider eliminating?
- Outline a strategy for deleting independent variables in this case.
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