CHE 405 HW 9 | Complete Solution

CHE 405 HW 9
In class, we used a least squares approach to solve for regression coefficients to develop a simple linear regression model for the following data set:
Air Velocity
(cm/s)
20
60
100
140
180
220
260
300
340
380
Evaporation Coefficient
(mm2/s)
0.18
0.37
0.35
0.78
0.56
0.75
1.18
1.36
1.17
1.65
a. Plot the raw data (air velocity is the regressor variable, evaporation coefficient is the response variable). Does the appearance of the data suggest simple linear regression is a good way to model the relationship between air velocity and evaporation coefficient?
b. Use the least squares normal equations to confirm the values we calculated in class for the regression coefficients (𝛽̂
𝑜=0.069 and 𝛽̂1=0.00383)
c. Using Minitab, generate a fitted line plot of the data. You are also welcome to do this in Excel, but make sure you display the regression equation and R2 value on your plot. Confirm that the regression coefficients produced by the software match your hand calculations. State in words what the R2 value represents.
d. Construct a 95% confidence interval for the regression coefficient 𝛽𝑜
e. Test the hypothesis 𝛽1=0 versus 𝛽1≠0 at the 0.05 significance level. What do the results of this hypothesis test on the slope of the regression line tell you?
f. Construct a 95% confidence interval on the mean evaporation coefficient when the air velocity is 190 cm/s
g. Find a 95% prediction interval for a future observation on the evaporation coefficient when the air velocity is 190 cm/s. How does this interval differ from the one calculated in part (f), and why?
h. Calculate the residuals for this data set. Use software to produce plots to determine if the assumptions that; (1) the errors are normally distributed, and (2) the errors have constant variance, are reasonable.
Note: Feel free to submit one plot for parts (a) and (c), you do not need a different plot for each question