) Calculate the coefficient of determination r2=r2= For part (b), express your answer in percent form (i.e. 3.00% instead of 0.03) and round to 2 decimal places. (b) What percent of the variation in satisfaction scores cannot be explained by the variation in median rates? %% For part (c), round to 4 decimal places. (c) What is the slope of the regression equation?
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.
Is your overall satisfaction with a hotel room correlated with the cost of the room? Suppose that satisfaction scores (in percent) and the median room prices/rates (in Canadian dollars) were recorded for a sample of 12 hotels with the following results:
| Hotel | Median Rate | Score |
| Econo Lodge | 90 | 80 |
| Crossways | 75 | 75 |
| Comfort Inn | 105 | 90 |
| Twelve Months | 95 | 88 |
| Days Inn | 55 | 60 |
| Coast Inn | 85 | 82 |
| Best Western | 65 | 70 |
| Travelodge | 115 | 93 |
| Paradise | 145 | 95 |
| Motel 6 | 95 | 95 |
| Accent Inn | 135 | 90 |
| Holiday Inn | 80 | 85 |
60801001201405060708090Median RateScore
Let us use the simple linear regression model taking the median rate as xx and the satisfaction score as yy. The coefficient of
ˆy=51.9368+0.3331xy^=51.9368+0.3331x.
For part (a), round to 4 decimal places.
(a) Calculate the coefficient of determination r2=r2=
For part (b), express your answer in percent form (i.e. 3.00% instead of 0.03) and round to 2 decimal places.
(b) What percent of the variation in satisfaction scores cannot be explained by the variation in median rates? %%
For part (c), round to 4 decimal places.
(c) What is the slope of the regression equation?
For parts (d), (e) round to 2 decimal places.
(d) How much will the score be expected to change if the median rate increases by $10?
(e) What would be the best predicted satisfaction score for the median rate of $120?
(f) Would it be possible to use this regression model to predict the satisfaction score for a hotel with the median room price of $500?
- The forecast would be reliable, as the regression equation ˆy=51.9368+0.3331xy^=51.9368+0.3331x can be used to predict any score.
- The forecast would not be reliable, as the median room price of $500 is an outlier.
- The forecast would be reliable, as the regression equation ˆy=51.9368+0.3331xy^=51.9368+0.3331x can be used to predict any room price.
- The forecast would be reliable, as the median room price of $500 is an outlier.
- None of the above.
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