In a simple linear regression, the following information is given:
= − 25; = 56;
a. | Calculate b1. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) |
b. | Calculate b0. (Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.) |
c-1. | What is the sample regression equation? (Negative value should be indicated by a minus sign. Round your answers to 2 decimal places.) |
c-2. | Predict y if x equals −20. (Round intermediate coefficient values and final answer to 2 decimal places.) |
2. In a simple linear regression, the following sample regression equation is obtained: | | y-hat = 436 − 17x. |
a. | Interpret the slope coefficient. | | | | | | As x increases by 1 unit, y is predicted to decrease by 436 units. | | | As x increases by 1 unit, y is predicted to decrease by 17 units. | | | As x increases by 1 unit, y is predicted to increase by 436 units. | | | As x increases by 1 unit, y is predicted to increase by 17 units. |
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b. | Predict y if x equals −15. |
3. Consider the following sample data: |
| | | | | | | | | x | 12 | 23 | 11 | 23 | 14 | 21 | 18 | 16 | y | 28 | 43 | 21 | 40 | 33 | 41 | 37 | 32 |
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Click here for the Excel Data File
b. | Calculate b1 and b0. What is the sample regression equation? (Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.) |
c. | Find the predicted value for y if x equals 10, 15, and 20. (Round intermediate coefficient values and final answer to 2 decimal places.) |
| y-hat | If x = 10 | | If x = 15 | | If x = 20 | |
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4. Consider the following sample data: |
| | | | | | | | | x | 22 | 24 | 27 | 21 | 23 | 14 | 14 | 15 | y | 101 | 139 | 250 | 88 | 87 | 14 | 16 | 20 |
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Click here for the Excel Data File
b. | Calculate b1 and b0. What is the sample regression equation? (Negative values should be indicated by a minus sign. Round intermediate calculations to 4 decimal places and final answers to 2 decimal places.) |
c. | Find the predicted value for y if x equals 15, 20, and 25. (Round intermediate coefficient values and final answers to 2 decimal places.) |
| y-hat | If x = 15 | | If x = 20 | | If x = 25 | |
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5. A social scientist would like to analyze the relationship between educational attainment and salary. He collects the following sample data, where Education refers to years of higher education and Salary is the individual’s annual salary in thousands of dollars: |
| | | | | | | | | Education | 3 | 4 | 6 | 2 | 5 | 4 | 8 | 0 | Salary | $40 | 53 | 80 | 42 | 70 | 50 | 110 | 38 |
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Click here for the Excel Data File
a. | Find the sample regression equation for the model: Salary = β0 + β1Education + ε. (Round intermediate calculations to 4 decimal places. Enter your answers in thousands rounded to 2 decimal places.) |
b. | Interpret the coefficient for Education. | | | | | | As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $8,590. | | | As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $9,380. | | | As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $8,590. | | | As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $9,380. |
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c. | What is the predicted salary for an individual who completed 7 years of higher education? (Round intermediate coefficient values to 2 decimal places and final answer, in dollars, to the nearest whole number.) |
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