Observations are taken on sales of a certain mountain bike in 24 sporting goods stores. The regression model was Y = total sales (thousands of dollars), X1 = display floor space (square meters), X2 = competitors' advertising expenditures (thousands of dollars), X3 = advertised price (dollars per unit). (a) Fill in the values in the table given here. (Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your t-values to 3 decimal places and p-values to 4 decimal places.) Predictor Coefficient SE tcalc p-value Intercept 1,272.5 361.9 FloorSpace 11.590 1.06 Competing Ads -6.697 3.938 Price -0.14802 0.08391 (b-1) What is the critical value of Student's t in Appendix D for a two-tailed test at α = .01? (Round your answer to 3 decimal places.) t-value =
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.
Observations are taken on sales of a certain mountain bike in 24 sporting goods stores. The regression model was Y = total sales (thousands of dollars), X1 = display floor space (square meters), X2 = competitors' advertising expenditures (thousands of dollars), X3 = advertised price (dollars per unit).
(a) Fill in the values in the table given here. (Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your t-values to 3 decimal places and p-values to 4 decimal places.)
| Predictor | Coefficient | SE | tcalc | p-value |
| Intercept | 1,272.5 | 361.9 | ||
| FloorSpace | 11.590 | 1.06 | ||
| Competing Ads | -6.697 | 3.938 | ||
| Price | -0.14802 | 0.08391 | ||
(b-1) What is the critical value of Student's t in Appendix D for a two-tailed test at α = .01? (Round your answer to 3 decimal places.)
t-value =
(a)
The tcalc formula is,
The t calculated values are,
| Predictor | Coefficient | SE | tcalc |
| Intercept | 1272.5 | 361.9 | |
| FloorSpace | 11.59 | 1.06 | |
| Competing Ads | -6.697 | 3.938 | |
| Price | -0.14802 | 0.08391 |
The degrees of freedom is,
The degrees of freedom is 20.
For Intercept:
The hypothesis is two tailed. The probability of t not equal to 3.516 with 20 degrees of freedom can be obtained using the excel formula “=T.DIST.2T(3.516,20)”. The p-value is 0.0022.
For FloorSpace:
The hypothesis is two tailed. The probability of t not equal to 10.934 with 20 degrees of freedom can be obtained using the excel formula “=T.DIST.2T(10.934,20)”. The p-value is 0.0000.
For Competing Ads:
The hypothesis is two tailed. The probability of t not equal to -1.701 with 20 degrees of freedom can be obtained using the excel formula “=T.DIST.2T(1.701,20)”. The p-value is 0.1044.
For Price:
The hypothesis is two tailed. The probability of t not equal to -1.764 with 20 degrees of freedom can be obtained using the excel formula “=T.DIST.2T(1.764,20)”. The p-value is 0.0930.
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