Click to see additional instructions Suppose we estimate a regression of the gallons of paint sold on the price of each gallon and find the following estimated regression line: y = 268.7 - 18.217x. a. Predict how many gallons would be sold if the price is $8 per gallon? gallons. b. If I have a sale and lower the price by $3, how many more gallons will I sell? I will sell additional gallons of paint. OMark for Review What's This?

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter2: Mathematics For Microeconomics
Section: Chapter Questions
Problem 2.16P
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SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
0.420882
"A"
0.160348
178,7876
51
ANOVA
df
MS
F
Significance F
337183.1884 337183.2 10.54851 0.002102099
Regression
Residual
Total
49
1566285.432 31965.01
50
1903468,62
Coefficients Standard Error t Stat
24.39789 113.8998288 0.214205 0.831276 -204.4923823 253.2881686
53.34785 16.42560445 3.247847 0.002102 20.33935972 86.35633563
P-value
Lower 95%
Upper 95%
Intercept
Unemployment
Click to see additional instructions
I estimate a regression of the number of violent crimes per 100,000
population on the unemployment rate for 50 states in the US plus the District
of Columbia. Therefore, there are n=51 observations. The output from this
regression is attached.
What is the R-squared statistic? It is
What percentage of variation in violent crime rates can be explained by the
variation in unemployment rate? The percenatge is
%.
Question 5 of 8
Click to see additional instructions
Suppose we estimate a regression of the gallons of paint sold on the price of
each gallon and find the following estimated regression line:
y = 268.7 - 18.217x.
a. Predict how many gallons would be sold if the price is $8 per gallon?
gallons.
b. If I have a sale and lower the price by $3, how many more gallons will I sell?
I will sell
additional gallons of paint.
Mark for Review What's This?
Question 6 of 8
Click to see additional instructions
The method of Least Squares (OLS) fits the line to the data points by minimizing
the sum of squared errors (SSE), also called the sum of squared residuals.
Remember that a residual is the difference between the observed yi value and the
corresponding predicted value from the regression line.
If the regression line = 2 + 3x has been fitted to the data points (4, 3), (5, 1), and
(1, 2), the residual sum of squares will be
O Mark for Review What's This?
Transcribed Image Text:SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.420882 "A" 0.160348 178,7876 51 ANOVA df MS F Significance F 337183.1884 337183.2 10.54851 0.002102099 Regression Residual Total 49 1566285.432 31965.01 50 1903468,62 Coefficients Standard Error t Stat 24.39789 113.8998288 0.214205 0.831276 -204.4923823 253.2881686 53.34785 16.42560445 3.247847 0.002102 20.33935972 86.35633563 P-value Lower 95% Upper 95% Intercept Unemployment Click to see additional instructions I estimate a regression of the number of violent crimes per 100,000 population on the unemployment rate for 50 states in the US plus the District of Columbia. Therefore, there are n=51 observations. The output from this regression is attached. What is the R-squared statistic? It is What percentage of variation in violent crime rates can be explained by the variation in unemployment rate? The percenatge is %. Question 5 of 8 Click to see additional instructions Suppose we estimate a regression of the gallons of paint sold on the price of each gallon and find the following estimated regression line: y = 268.7 - 18.217x. a. Predict how many gallons would be sold if the price is $8 per gallon? gallons. b. If I have a sale and lower the price by $3, how many more gallons will I sell? I will sell additional gallons of paint. Mark for Review What's This? Question 6 of 8 Click to see additional instructions The method of Least Squares (OLS) fits the line to the data points by minimizing the sum of squared errors (SSE), also called the sum of squared residuals. Remember that a residual is the difference between the observed yi value and the corresponding predicted value from the regression line. If the regression line = 2 + 3x has been fitted to the data points (4, 3), (5, 1), and (1, 2), the residual sum of squares will be O Mark for Review What's This?
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