Shown below is a portion of a computer output for a linear regression analysis relating y (demand in units) and x (unit price in $). Coefficient Standard Error t-statistic p-value Intercept 80.390 3.102 25.916 0.000 x –2.137 0.248 ? 0.000 Source of Variation Sum of squares Degrees of freedom Mean square F-statistic p-value Regression 5048.818 1 5048.818 ? ? Error ? 46 ? Total 8181.479 47 We are interested in determining whether or not demand and unit price are linearly related using a significance level α = 0.05 . a. Fully interpret the meaning of the estimated coefficient of x in this estimated linear regression equation. b. Complete the missing values in the regression output tables above. c.Calculate the coefficient of determination, r2, and fully interpret its meaning in this context. Be very specific
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
- Shown below is a portion of a computer output for a linear
regression analysis relating y (demand in units) and x (unit price in $).
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|
Coefficient |
Standard Error |
t-statistic |
p-value |
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|
Intercept |
80.390 |
3.102 |
25.916 |
0.000 |
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|||||
|
|
x |
–2.137 |
0.248 |
? |
0.000 |
|
|||||
|
Source of Variation |
Sum of squares |
Degrees of freedom |
Mean square |
F-statistic |
p-value |
||||||
|
Regression |
5048.818 |
1 |
5048.818 |
? |
? |
||||||
|
Error |
? |
46 |
? |
|
|
||||||
|
Total |
8181.479 |
47 |
|
|
|
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We are interested in determining whether or not demand and unit price are linearly related using a significance level α = 0.05 .
a. Fully interpret the meaning of the estimated coefficient of x in this estimated linear regression equation.
b. Complete the missing values in the regression output tables above.
c.Calculate the coefficient of determination, r2, and fully interpret its meaning in this context. Be very specific.
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