The number of pounds of steam used per month at a plant is thought to be related to the average monthly ambient temperature. Following is the past year's (Jan. -Dec.) usages and temperature data. Fit a simple linear regression model to the data and test for significance of the model.
Steam, lb 186 215 288 425 455 539 622 675 562 453 370 274
Temperature 21 24 32 47 50 59 68 74 62 50 41 30
Answer the following questions, including the graphs from Minitab.
1. Use a scatterplot in order to explain the relationship between X and Y [login to view URL] do you expect for the sign of beta1 and magnitude of r2? 2. After running the regression model in Minitab: [login to view URL] is the estimated regression equation? 1. Interpret the estimate of 훽0 in the words of the problem. Do the same for 훽1. 훽0 = 1.49. 2. Conduct a test that the true slope of the model differs from 0. 3. Explain how to use the output of the regression for the test. [login to view URL] the conclusion of your test to the scatterplot that you generated in (1) b. Use the generated plots of the regression model (histogram of the residuals) in order to check the normality assumption of your model. While there is no need for a statistical test, you must compare the shape to a normal distribution pdf. 4. Generate the fitted line plot for this regression 5. Generate prediction interval for y* and confidence interval for (x) when x* = x(x average of given x’s). Note that x* is a point in units that we are interested in predicting the Minutes for it. Here, as an example, we use x = 6 (average of column “unit”) as x*. So in general you can pick any value for x*. For generating the intervals, we need to run the regression model again.