Researchers measured oxygen co

Researchers measured oxygen consumption in 10 seals. Theymeasured 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 asnonfeeding dives).   They wanted to learn about therelationship between oxygen consumption for feeding dives andoxygen consumption for nonfeeding dives so they fit a linearregression model with Y = Oxygen consumption in feeding dive and X= Oxygen consumption in nonfeeding dive. The model was fit in R andthe 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 ***

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.
  1. Provide an interpretation of the estimated slope of theregression line.
  1. Use the regression equation to estimate the oxygen consumptionfor a feeding dive for a seal for which the oxygen consumption in anonfeeding dive is 80.0.

Answer:

Answer a)

From the regression output, we can see that intercept = 16.7693and 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 isa positive or negative correlation between each independentvariable the dependent variable. A positive coefficient indicatesthat as the value of the independent variable increases, the meanof the dependent variable also tends to increase.  Inthis case, the value of slope (Regression coefficient of X) ispositive, this shows that for each unit increase in Oxygenconsumption in nonfeeding dive, Oxygen consumption in feeding diveincreases by 1.2010 units.

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

Answer c)

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

Y = 16.7693 + 1.2010*80

Y = 112.8493


 
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