8.SP.A.3
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
Example Problems
Zara studied the age (in years) and resale value (in thousand dollars) of a random sample of 40 used cars. Here is computer output on the sample data:
Regression: resale value vs. age
Assume that all conditions for inference have been met.
Write the expression for the test statistic for testing the null hypothesis that the population slope in this setting is .
Regression: resale value vs. age
| Predictor | Coef | SE Coef |
|---|---|---|
| Constant | 18.7 | 0.9 |
| Age | -1.85 | 0.31 |
Assume that all conditions for inference have been met.
Write the expression for the test statistic for testing the null hypothesis that the population slope in this setting is .
Leona collected data on the battery life (in hours) and price (in dollars) of a random sample of mobile phones. Here is computer output from a least-squares regression analysis on her sample:
Assume that all conditions for inference have been met.
Write the expression for the test statistic for testing the null hypothesis that the population slope in this setting is 0.
| Predictor | Coef | SE Coef |
|---|---|---|
| Constant | 191.312 | 94.318 |
| Battery life | 6.556 | 3.788 |
Assume that all conditions for inference have been met.
Write the expression for the test statistic for testing the null hypothesis that the population slope in this setting is 0.
Mateo collected data on students' heights (in ) and their vertical jump heights (in ) for a random sample of 35 athletes. Here is computer output on the sample data:
Regression: vertical jump vs. height
Assume that all conditions for inference have been met.
Write the expression for the test statistic for testing the null hypothesis that the population slope in this setting is ?
Regression: vertical jump vs. height
| Predictor | Coef | SE Coef |
|---|---|---|
| Constant | -14.3 | 22.8 |
| Height | 0.12 | 0.07 |
Assume that all conditions for inference have been met.
Write the expression for the test statistic for testing the null hypothesis that the population slope in this setting is ?
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