Please see problem with the solution: after reviewing the information below, assess the appropriateness and accuracy of using a linear regression model. Discuss the meaning of the standard error of the estimate and how it affects the predicted values of Y for that analysis. Many people are also using online shopping to avoid going to stores in person. I decided to use my own data. I am going to add how many Amazon transactions I have made each month from March- August. X= the month Y= amount of purchases Simple linear regression results: Dependent Variable: sale Independent Variable: month sale = 0.53333333 + 1.6 month Sample size: 6 R (correlation coefficient) = 0.99410024 R-sq = 0.98823529 Estimate of error standard deviation: 0.36514837 Parameter estimates: Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 0.53333333 0.50269117 ≠ 0 4 1.0609562 0.3485 Slope 1.6 0.087287156 ≠ 0 4 18.330303 <0.0001 Analysis of variance table for regression model: Source DF SS MS F-stat P-value Model 1 44.8 44.8 336 <0.0001 Error 4 0.53333333 0.13333333 Total 5 45.333333
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.
Please see problem with the solution: after reviewing the information below, assess the appropriateness and accuracy of using a linear regression model. Discuss the meaning of the standard error of the estimate and how it affects the predicted values of Y for that analysis.
Many people are also using online shopping to avoid going to stores in person. I decided to use my own data. I am going to add how many Amazon transactions I have made each month from March- August.
X= the month
Y= amount of purchases
Simple linear regression results:
Dependent Variable: sale
Independent Variable: month
sale = 0.53333333 + 1.6 month
R (
R-sq = 0.98823529
Estimate of error standard deviation: 0.36514837
Parameter estimates:
|
Parameter |
Estimate |
Std. Err. |
Alternative |
DF |
T-Stat |
P-value |
|
Intercept |
0.53333333 |
0.50269117 |
≠ 0 |
4 |
1.0609562 |
0.3485 |
|
Slope |
1.6 |
0.087287156 |
≠ 0 |
4 |
18.330303 |
<0.0001 |
Analysis of variance table for regression model:
|
Source |
DF |
SS |
MS |
F-stat |
P-value |
|
Model |
1 |
44.8 |
44.8 |
336 |
<0.0001 |
|
Error |
4 |
0.53333333 |
0.13333333 |
||
|
Total |
5 |
45.333333 |
The important results that can be seen in the analysis are,
1)R-Sq
2)estimate of error standard deviation ,
3) p-value in the ANOVA table for regression model.
The average distance between the regression line and the observed values is termed as standard error of the estimate .If the observations are closer to the fitted line then its values will be small. Thus smaller values of estimate of error standard deviation is required. With increase in its value one gets wrong predictions.
the coefficient of determination, denoted R² or r² and pronounced "R squared", is the proportion of the variance in the dependent variable that is predictable from the independent variable.
R2 OR R-Sq is termed as coefficient of determination and in a regression model it measures the proportion of variance present in dependent variable that is explained by independent variable(s).
A statistic for testing hypothesis that all regression coefficients not equal to zero against the hypothesis that all regression coefficients equal to zero (Null Hypothesis).Smaller p-value gives strong evidence for rejection of null hypothesis.
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