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Author Question: What is the relationship between diamond price and carat size? 307 diamonds were sampled and a ... (Read 41 times)

luvbio

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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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Marked as best answer by luvbio on Feb 14, 2020

samiel-sayed

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luvbio

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Reply 2 on: Feb 14, 2020
Excellent


diana chang

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Reply 3 on: Yesterday
Great answer, keep it coming :)

 

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