Question

Researchers measured oxygen consumption in 10 seals. They measured oxygen consumption for each seal under two conditions: (1) when they did a dive for food (referred to as a feeding dive) and (2) when they did a dive that was not food-related (referred to as nonfeeding dives).   They wanted to learn about the relationship between oxygen consumption for feeding dives and oxygen consumption for nonfeeding dives so they fit a linear regression model with Y = Oxygen consumption in feeding dive and X = Oxygen consumption in nonfeeding dive. The model was fit in R and the results are given below:

Coefficients:

   Estimate    Std. Error t value    Pr(>|t|)

Intercept    16.7693    8.6483 1.939 0.0885 .

OxygenNonfeeding 1.2010 0.1124 10.681 5.18e-06 ***

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Residual standard error: 6.542 on 8 degrees of freedom

Multiple R-squared: 0.9345,Adjusted R-squared: 0.9263

F-statistic: 114.1 on 1 and 8 DF, p-value: 5.18e-06

1. Write down the estimated regression line.

2. Provide an interpretation of the estimated slope of the regression line.

3. Use the regression equation to estimate the oxygen consumption for a feeding dive for a seal for which the oxygen consumption in a nonfeeding dive is 80.0.

Answer 1

Answer a)

From the regression output, we can see that intercept = 16.7693 and value of slope that is coefficient of Oxygen Nonfeeding = 1.2010. So, we can write regression equation as:

Y = 16.7693 + 1.2010*X

Answer b)

Interpretation of Slope:

The sign of a regression coefficient tells you whether there is a positive or negative correlation between each independent variable the dependent variable. A positive coefficient indicates that as the value of the independent variable increases, the mean of the dependent variable also tends to increase.  In this case, the value of slope (Regression coefficient of X) is positive, this shows that for each unit increase in Oxygen consumption in nonfeeding dive, Oxygen consumption in feeding dive increases by 1.2010 units.

If the p-value for a variable is less than your significance level, your sample data provide enough evidence to reject the null hypothesis for the entire population. Your data favor the hypothesis that there is a non-zero correlation. In this case, p-value corresponding to Regression coefficient of X (Oxygen consumption in nonfeeding dive) is less than 0.05 significance level so we can say that Oxygen consumption in nonfeeding dive is a significant predictor of Oxygen consumption in feeding dive.

Answer c)

At X = 80, the oxygen consumption for a feeding dive can be estimated using regression equation:

Y = 16.7693 + 1.2010*80

Y = 112.8493