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.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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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