Question 1
Consider the data set shown below. Find the standard deviation of the least squares regression line.
◦ 0.94643
◦ 1.49045
◦ 1.5
◦ 0.9003
Question 2
What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between y = diamond price (in dollars) and x = size of the diamond (in carats). The simple linear regression for the analysis is shown below:
Least Squares Linear Regression of PRICE
Predictor
Variables Coefficient Std Error T P
Constant
-2298.36
158.531
-14.50
0.0000
Size
11598.9
230.111
50.41
0.0000
R-Squared
0.8925
Resid. Mean Square (MSE)
1248950
Adjusted R-Squared
0.8922
Standard Deviation
1117.56
Interpret the standard deviation of the regression model.
◦ We can explain 89.25% of the variation in the sampled diamond prices around their mean using the size of the diamond in a linear model.
◦ We expect most of the sampled diamond prices to fall within $2235.12 of their least squares predicted values.
◦ We expect most of the sampled diamond prices to fall within $1117.56 of their least squares predicted values.
◦ For every 1-carat increase in the size of a diamond, we estimate that the price of the diamond will increase by $1117.56.
Metabolic rates of animals that differ in size.
Relationship between fruit radius and beak length in populations of native and introduced species of
Size comparison of Earth and Mars.
Size comparison of Earth and Uranus
Frontispiece, Diamond Sutra, from Cave 17, Dunhuang.
Relationship Between the Atlas and the Axis. The Dens of the Axis Provides a Pivotal Point Around Wh