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.
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