A Simple Linear Regression (SLR) was performed where the monthly Revenue ("Rev", the y-variable) was regressed on the monthly Advertising Expenditures ("Expend", the x-variable). Excel was used to construct the 98% Confidence Interval (CI) estimate of B1. The Excel-generated Regression output is provided below: ANOVA df SS MS F Significance F Regression 1 492.528125 492.528125 10.65525634 0.046980871 Residual 3 138.671875 46.22395833 Total 4 631.2 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 98.0% Upper 98.0% Intercept 23.1328125 5.324310936 4.344752359 0.022510469 6.188478833 40.07714617 -1.043301388 47.30892639 Expend 3.1015625 0.950164031 3.264239014 0.046980871 0.077716489 6.125408511 -1.212850033 7.415975033 a. Enter the value of the Left-Hand Endpoint (LHEP) of the 98% Confidence Interval (CI) estimate of B1 . Round off your answer to the fourth decimal place. The LHEP of the 98% CI for B1, rounded off as instructed, is: _________________________ b. Enter the value of the Right-Hand Endpoint (RHEP) of the 98% Confidence Interval (CI) estimate of B1. Round off your answer to the fourth decimal place. The RHEP of the 98% CI for B1 , rounded off as instructed, is: _______________ c. Select the number of the following statement that gives the correct interpretation of the CI in this problem: 1: the CI is a NEGATIVE CI, and therefore REV and EXPEND are NOT significantly Linearly related. 2: The CI is a POSITIVE CI, and therefore REV and EXPEND are NOT significantly Linearly related. 3: The CI is a MIXED CI, and therefore REV and EXPEND are NOT significantly Linearly related. 4: The CI is a NEGATIVE CI, and therefore REV and EXPEND ARE significantly Negatively Linearly related. 5: The CI is a POSITIVE CI, and therefore REV and EXPEND ARE significantly Positively Linearly related. Answer to part (c): _______________
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.
A Simple Linear Regression (SLR) was performed where the monthly Revenue ("Rev", the y-variable) was regressed on the monthly Advertising Expenditures ("Expend", the x-variable). Excel was used to construct the 98% Confidence
| ANOVA | ||||||||
| df | SS | MS | F | Significance F | ||||
| Regression | 1 | 492.528125 | 492.528125 | 10.65525634 | 0.046980871 | |||
| Residual | 3 | 138.671875 | 46.22395833 | |||||
| Total | 4 | 631.2 | ||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 98.0% | Upper 98.0% | |
| Intercept | 23.1328125 | 5.324310936 | 4.344752359 | 0.022510469 | 6.188478833 | 40.07714617 | -1.043301388 | 47.30892639 |
| Expend | 3.1015625 | 0.950164031 | 3.264239014 | 0.046980871 | 0.077716489 | 6.125408511 | -1.212850033 | 7.415975033 |
a. Enter the value of the Left-Hand Endpoint (LHEP) of the 98% Confidence Interval (CI) estimate of B1 . Round off your answer to the fourth decimal place.
The LHEP of the 98% CI for B1, rounded off as instructed, is:
_________________________
b. Enter the value of the Right-Hand Endpoint (RHEP) of the 98% Confidence Interval (CI) estimate of B1. Round off your answer to the fourth decimal place.
The RHEP of the 98% CI for B1 , rounded off as instructed, is: _______________
c. Select the number of the following statement that gives the correct interpretation of the CI in this problem:
1: the CI is a NEGATIVE CI, and therefore REV and EXPEND are NOT significantly Linearly related.
2: The CI is a POSITIVE CI, and therefore REV and EXPEND are NOT significantly Linearly related.
3: The CI is a MIXED CI, and therefore REV and EXPEND are NOT significantly Linearly related.
4: The CI is a NEGATIVE CI, and therefore REV and EXPEND ARE significantly Negatively Linearly related.
5: The CI is a POSITIVE CI, and therefore REV and EXPEND ARE significantly Positively Linearly related.
Answer to part (c): _______________
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