Consider a marketer who develops a simple regression model to explain the costs of flighting (Y) by the number of passengers (X), for 12 commercial airline flights during the covid-19 crisis. He uses the sample Y intercept b0, and the sample slope b1, as estimates of the respective population parameters. You are asked to help this marketer to make his estimation. SHOW ALL YOUR CALCULATIONS IN DETAIL Number of passengers Cost (thousands $) 61 4.280 63 4.080 67 4.420 69 4.170 70 4.480 74 4.300 76 4.820 81 4.700 86 5.110 91 5.130 95 5.640 97 5.560
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.
Consider a marketer who develops a simple regression model to explain the costs of flighting (Y) by the number of passengers (X), for 12 commercial airline flights during the covid-19 crisis. He uses the sample Y intercept b0, and the sample slope b1, as estimates of the respective population parameters.
You are asked to help this marketer to make his estimation.
SHOW ALL YOUR CALCULATIONS IN DETAIL
|
Number of passengers |
Cost (thousands $) |
|
61 |
4.280 |
|
63 |
4.080 |
|
67 |
4.420 |
|
69 |
4.170 |
|
70 |
4.480 |
|
74 |
4.300 |
|
76 |
4.820 |
|
81 |
4.700 |
|
86 |
5.110 |
|
91 |
5.130 |
|
95 |
5.640 |
|
97 |
5.560 |
- Use a 95% confidence interval for β1 to test the hypotheses just run in the t test. Do you confirm your conclusions about the significance of β1? Explain your answer.
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