ffice Construction Month Apr May Jun Jul Aug Sep Amount (in thousands) $15 $25 $42 $51 $60 $74The following data show the amount spent on office-building construction (in thousands) for a particular county during a 6-month period. Find the least‑squares regression line
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.
| Month | Apr | May | Jun | Jul | Aug | Sep |
|---|---|---|---|---|---|---|
| Amount (in thousands) | $15 | $25 | $42 | $51 | $60 | $74 |
- Find the least‑squares regression line for the data. (Let x=1 correspond to January, x=2to February, etc.) Round the coefficients to three decimal places.
- Estimate the amount spent on construction in October. Express your answer in thousands of dollars and round to three decimal places.
1.
Least-squares regression line:
Let x=1 correspond to January, x=2 correspond to February
Given information:
| x | y |
| 4 | 15 |
| 5 | 25 |
| 6 | 42 |
| 7 | 51 |
| 8 | 60 |
| 9 | 74 |
Excel Procedure:
Enter X and Y in Excel>Data>Data Analysis> ‘Regression’>Select Y under ‘Input Y Range’>Select X under ‘Input X Range’>Click on ‘OK’.
Output:
From the output,
The regression equation is y=-31.457+11.686x
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