20 May The Correlation Between Two Variables
- For each of the following, determine whether the correlation between two variables is significantly different from zero, i.e.,
versus
- A biologist is studying the levels of heavy metal contaminants among a population of the South Nakaratuan Chubby Bat. The biologist is interested in constructing a simple linear regression model to investigate the relationship between weight of an animal and the level of heavy metal contamination. In the proposed regression model the level of contaminant is the response variable and weight is the explanatory variable. The contaminant level is measured in parts per billion (ppb) and weight in grams. The SPSS output is given below. Use the output to answer the following questions.
| Model Summary | ||||||||||
| Model | R | R Square | Adjusted R Square | Std. Error of the Estimate | ||||||
| 1 | .921a | .848 | .839 | 13.82229 | ||||||
| a. Predictors: (Constant), weight | ||||||||||
| ANOVAa | ||||||||||
| Model | Sum of Squares | df | Mean Square | F | Sig. | |||||
| 1 | Regression | 18143 | 1 | 18143 | 94.96 | .000b | ||||
| Residual | 3247.94781 | 17 | 191.05575 | |||||||
| Total | 21391 | 18 | ||||||||
| a. Dependent Variable: contaminant | ||||||||||
| b. Predictors: (Constant), weight | ||||||||||
| Coefficientsa | ||||||
| Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | ||
| B | Std. Error | Beta | ||||
| 1 | (Constant) | -71.63611 | 28.17794 | -2.54 | .021 | |
| weight | 2.18277 | 0.22399 | .921 | 9.74 | .000 | |
| a. Dependent Variable: contaminant | ||||||
-
- What percent of variation in the values of contaminant level that is explained by the linear regression model between contaminant level and weight?
- What is the correlation between contaminant level and weight?
- What is the predicted contaminant level for an animal weighted 150 grams?
- One of the animals in this analysis had a weight of 145 grams and contaminant level of 222 ppb. What is the residual for this observation?
- What is least squares regression line?
- What is the average change in contaminant level when the weight of an animal is increased by 1 gram?
- Construct a 99% confidence interval for the regression slope.
- The biologist wants to determine whether there is a positive linear association between contaminant level and weight of an animal. Write down the appropriate hypotheses, value of test statistic, degrees of freedom of the test statistic, p-value, and the conclusion.
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