The article “Multiple Linear Regression for Lake Ice and Lake Temperature Characteristics” (S. Gao and H. Stefan, Journal of Cold Regions Engineering, 1999:59-77) presents data on maximum ice thickness in mm (y), average number of days per year of ice cover (x1), average number of days the bottom temperature is lower than 8°C (x2), and the average snow depth in mm (x3) for 13 lakes in Minnesota. The data are presented in the following table.

a. Fit the model y =β0 + β1x1 + β2x2 + ε. For each coefficient, find the P-value for testing the null hypothesis that the coefficient is equal to 0.

b. If two lakes differ by 2 in the average number of days per year of ice cover, with other variables being equal, by how much would you expect their maximum ice thicknesses to differ?

c. Do lakes with greater average snow depth tend to have greater or lesser maximum ice thickness? Explain.

Week 2: Data Confidence of Distributions Using Mean, and Standard Deviations What is measurement distribution, and why is it important • In experiments in analytical chemistry, we are trying to find the true value of the subject of observation • Measurement distribution is when a number is reported as a true value plus or minus some error o We can never know the true value of a distribution, but we can test in a way where we get close o The bigger the range of numbers, the less precise