Math 10 - Lab 11ANOVA & Regression

For questions 1, use the file RateMP.mpj and the MINITAB command ANOVAONEWAY. Make sure you choose the Comparisons option and select the Tukey test.

  1. You want to test the hypothesis: is there a difference in overall quality due to Division. There are five divisions (some were combined): Certificate Programs/Other, Creative Arts/Physical Ed, Social Studies/Humanities/Business, Language/International/Multicultural, Physical and Health Science
  1. What is response and what is the factor? How many levels?
  1. State the hypothesesin words and parameters.
  1. Run the appropriate one factor ANOVA test. Make sure you select the Tukey Test under the Comparisons options. Paste the results here, including a graph comparing the means.
  1. State a detailed conclusion using the both ANOVA results and the Tukey Test results.

Open the file Calrainfall.MPJ which represents average annual precipitation (rainfall) in inches and other numeric data about some California Cities: Latitude in degrees north, Altitude above sea level in feet, and distance from coast in miles. Use the command Regression>Fitted Line Plot for Scatterplots, Regression Line, r2 and Hypothesis test. Use the command Regression>Regression for residuals and predictions. Unless otherwise specified, conduct all hypothesis tests with  = 0.05

  1. You will design a regression Model where Latitude is the Independent variable and Precipitation is the response. Run Minitab Stat>Regression>Fitted Line Plot
  1. Make a scatterplot and graph the least square line.Interpret the slope.
  1. Conduct the appropriate hypothesis test for a significant correlation between precipitation and latitude.
  1. Find and interpret r2.
  1. Run Minitab Stat>Regression>Regression>Fit Regression Model. Then find a 95% confidence interval for the expected precipitation for a city at latitude 40 degrees north using
    Stat>Regression>Regression>Predict.

  1. You will design a regression Model where Altitude is the Independent variable and Precipitation is the response. Run Minitab Stat>Regression>Fitted Line Plot
  1. Make a scatterplot and graph the least square line.Interpret the slope.
  1. Conduct the appropriate hypothesis test for a significant correlation between precipitation and altitude.
  1. Find and interpret r2.
  1. Run Minitab Stat>Regression>Regression>Fit Regression Model. Click Results and change Fits and Diagnostics to for all observations.

Then find a 95% prediction interval for the precipitation for a city at altitude of 150 feet using
Stat>Regression>Regression>Predict.

  1. Analyze the residuals. Which city fits the model best? Which city fits the model worst?

  1. You will design a regression Model where Distance from Coast is the Independent variable and Precipitation is the response. Run Minitab Stat>Regression>Fitted Line Plot
  1. Make a scatterplot and graph the least square line. Interpret the slope.
  1. Conduct the appropriate hypothesis test for a significant correlation between precipitation and distance from coast.
  1. Find and interpret r2.
  1. Looking at the scatterplot, it seems that a non-linear regression model might be a better fit for precipitation and distance from coast. Rerun the fitted line plot but choose cubic instead on linear. Paste the graph here. Under this model, what percentage of the variability precipitation is explained by distance from coast?