The data resulting from a random sample of 5 observations are shown below. Y is the dependent variable, and X1 and X2 are the independent variables. Observation Y X1 X2 1 87 95 11 2 86 94 11 3 84 94 11 4 83 93 12 5 84 93 12 Use Excel's Regression tool to answer the following questions. To copy the data set, highlight the table, press Ctrl-c, click on the Excel cell to which you want to copy, then press Ctrl-v. Fill in Multiple Blanks For all numerical answers, show one (1) digit to the right of the decimal point, for example, 1.0, 1.2. Apply the appropriate rounding rule if necessary. Hint: You can use the “Format Cell” option in the Regression output so that it shows two digits after the decimal point. Excel will automatically round the values up or down, if necessary. 1. The estimated regression line is (enter the estimated coefficients in the appropriate space): yhat = __________ + ________ X1 + ________________ X2 2. At 95% confidence, X1 _______ (enter is, is not) significantly related to Y. 3. At 95% confidence, X2 (enter is, is not) significantly related to Y. _____________
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.
Question 6
The data resulting from a random sample of 5 observations are shown below. Y is the dependent variable, and X1 and X2 are the independent variables.
|
Observation |
Y |
X1 |
X2 |
|
1 |
87 |
95 |
11 |
|
2 |
86 |
94 |
11 |
|
3 |
84 |
94 |
11 |
|
4 |
83 |
93 |
12 |
|
5 |
84 |
93 |
12 |
Use Excel's Regression tool to answer the following questions. To copy the data set, highlight the table, press Ctrl-c, click on the Excel cell to which you want to copy, then press Ctrl-v.
Fill in Multiple Blanks
For all numerical answers, show one (1) digit to the right of the decimal point, for example, 1.0, 1.2. Apply the appropriate rounding rule if necessary. Hint: You can use the “Format Cell” option in the Regression output so that it shows two digits after the decimal point. Excel will automatically round the values up or down, if necessary.
1. The estimated regression line is (enter the estimated coefficients in the appropriate space):
yhat = __________ + ________ X1 + ________________ X2
2. At 95% confidence, X1 _______ (enter is, is not) significantly related to Y.
3. At 95% confidence, X2 (enter is, is not) significantly related to Y. _____________
4. Predict Y when X1 = 94.8 and X2 = 11.2. Yhat = __________ .
5. While testing for overall significance at 95% confidence, the null hypothesis (shown below) (enter should, should not) ___________ be rejected.
Ho: beta1 = beta2 = 0
Ha: At least one of the beta's does not equal 0
6. True or false? About 77% of the variability in Y is explained by X1 and X2, and about 23% of the variability in Y is explained by the other factors not included in the regression. ______________ (Enter true, false).
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