A Statistics Project
Callini47
correlation.xlsDataCopy
| Variable | (X-XBar)^2 | ||
| 27.4 | 24.4 | 0 | |
| 27.2 | 25.5 | 0 | |
| 24.1 | 23 | 0 | |
| 22.7 | 20.2 | 0 | |
| 22.1 | 20.1 | 0 | |
| 18.3 | 17.5 | 0 | |
| 17.5 | 16.1 | 0 | |
| 17.5 | 13.3 | 0 | |
| 16.8 | 14.7 | 0 | |
| 16.5 | 13.6 | 0 |
Correlation
| Correlation & Regression | |||||||||
| Data | X-Data | Y-Data | |||||||
| Observation | Ads | Sales | REGRESSION STATISTICS | ||||||
| Obs 1 | 20 | 48 | Observations | 10 | |||||
| Obs 2 | 15 | 38 | Correlation coefficient (r) | 0.978 | |||||
| Obs 3 | 12 | 33 | Coefficient of determination (r-squared) | 96% | |||||
| Obs 4 | 32 | 65 | Standard error of the estimate | 3.469 | |||||
| Obs 5 | 17 | 40 | |||||||
| Obs 6 | 8 | 18 | REGRESSION EQUATION | ||||||
| Obs 7 | 10 | 25 | Slope | 2.017 | |||||
| Obs 8 | 16 | 35 | Intercept | 5.134 | |||||
| Obs 9 | 20 | 50 | Sales = 5.134 + 2.017 (Ads) | ||||||
| Obs 10 | 5 | 12 | |||||||
| Obs 11 | PREDICTING WITH THE REGRESSION EQUATION | ||||||||
| Obs 12 | X value | 20 | |||||||
| Obs 13 | Confidence Level | 95% | |||||||
| Obs 14 | Predicted Y value | 45.477 | |||||||
| Obs 15 | Confidence Interval | 45.477 | + | 2.978 | |||||
| Obs 16 | Prediction Interval | 45.477 | + | 8.535 | |||||
| Obs 17 | |||||||||
| Obs 18 | HYPOTHESIS TEST FOR CORRELATION | ||||||||
| Obs 19 | Null hypothesis: Slope = 0 (no correlation) | ||||||||
| Obs 20 | Level of Significance | 0.05 | |||||||
| Obs 21 | t-Statistic (computed) | 13.3189 | |||||||
| Obs 22 | p-value | 0.0000 | |||||||
| Obs 23 | Decision | Reject the null hypothesis | |||||||
| Obs 24 | Conclusion | Conclude that correlation exists. | |||||||
| Obs 25 | |||||||||
| Obs 26 | ANOVA | SS | df | MS | F | F crit | |||
| Obs 27 | Regression | 2134.1544 | 1 | 2134.1544 | 177.3924 | 5.3177 | |||
| Obs 28 | Error | 96.2456 | 8 | 12.0307 | |||||
| Obs 29 | Total | 2230.4000 | 9 | ||||||
| Obs 30 | |||||||||
| Obs 31 | |||||||||
| Obs 32 | CORRELATION GUIDELINES | ||||||||
| Obs 33 | Step 1: input the data (note which is the dependent variable) | ||||||||
| Obs 34 | Step 2: assess the scatter diagram for linearity (if not linear, STOP) | ||||||||
| Obs 35 | Step 3: hypothesis test for correlation (if correlation does not exist, STOP) | ||||||||
| Obs 36 | Step 4: evaluate regression statistics (if correlation is weak, reconsider its value) | ||||||||
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| Obs 40 | ©2007 DrJimMirabella.com | ||||||||
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&A
This is the measure of the degree of relationship between the X and Y variables. 1 is perfect, .70 to 1.00 is strong, .30 to .69 is moderate, less than .30 is weak, 0 means no correlation. The same rules apply to positive or negative correlations.
Also referred to as ALPHA. This is your tolerance for error; it is the probability of incorrectly rejecting the null hypothesis.
The X-data is the independent variable.
Enter up to 125 paired observations.
Enter the x-value that you want to use to predict the y-value. You should never input an X-value that is beyond the range of the data (i.e., it should be between the smallest and largest X-Data observation).
This is the predicted value using the x-value above and the regression equation.
This estimates the mean value of Y given X.
This estimates the range of values of Y for a given X and should be larger than the confidence interval.
This explains the percent of the variability in Y that can be explained by the regression equation.
This explains the degree of relationship between the dependent and independent variables.
Enter the confidence level to be used in the confidence and prediction intervals.
The X-data is the independent variable from which a prediction is made.
The Y-data is the dependent variable that is being predicted by the regression equation.
Also referred to as ALPHA. This is your tolerance for error; it is the probability of incorrectly rejecting the null hypothesis.
A one unit change in X results in a change in Y equal to the value of the slope.
A p-value is the probability of making a type 1 error if you reject the null hypothesis. In other words, it is the probability you would be making a mistake to reject the null.
A measure of dispersion of the data around the regression line. Similar to standard deviation, for a given prediction you would expect with 95% confidence that the prediction would be with 2 standard errors of the regression line.
ScatterDiagram
| Sales = 5.134 + 2.017 (Ads) | |||||||||
| Sales | |||||||||
| Ads | |||||||||
| r = 0.978 | r-squared = 0.957 |
ScatterDiagram
| 20 |
| 15 |
| 12 |
| 32 |
| 17 |
| 8 |
| 10 |
| 16 |
| 20 |
| 5 |
Sales
48
38
33
65
40
18
25
35
50
12
