Examining Relationships: Quantitative Data

Assignment: Scatterplot

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Question 1:Describe the relationship between the height and weight of the subjects. To describe the relationship write about the pattern (direction, form, and strength) and any deviations from the pattern (outliers).

The scatter plot shows the relationship between height and weight of the subjects to be positive, non-linear with a strong association. The data points appear clustered with no outliers.

Question 2: Compare and contrast the relationship between height and weight for males and females. To compare and contrast the relationships by gender write about the pattern (direction, form, and strength) and any deviations from the pattern (outliers) for each group.

The association between height and weight for females is positive, linear and weak with outliers while the association for males height against weight is positive, linear, weak and without outliers.

Discuss how the patterns for the two groups are similar and how they are different.

Both patterns for male and female have the same linear direction, their strength is weak and not clustered. However, female pattern has outliers on the left while males pattern seem to have no outliers.

Assignment: Linear RelationshipsQuestion 1:Report the correlation between gestation and longevity and comment on the strength and direction of the relationship. Interpret your findings in context.

The correlation between gestation and longevity is 0.66324. The relationship is moderately strong with a positive direction.

Now return to the scatterplot that you created earlier. Notice that there is an outlier in both longevity (40 years) and gestation (645 days). Note: This outlier corresponds to the longevity and gestation period of the elephant. What do you think will happen to the correlation if we remove this outlier?

If the outlier is removed, the relationship changes form moderately strong to strong and less scattered.

Question 2: Report the new value for the correlation between gestation and longevity and compare it to the value you found earlier when the outlier was included. What is it about this outlier that results in the fact that its inclusion in the data causes the correlation to increase? (Hint: look at the scatterplot

The new correlation value is 0.519039 . This outlier increases deviation of points that makes the correlation to increase.

Assignment: Linear RegressionQuestion 1: Give the equation for the least squares regression line, and interpret it in context.

The slope (b) = r (sy/sx).

r is the correlation,

sy is the standard deviation for y(time)

sx is the standard deviation for x (year)

r = -0.89075

sy = 14.55437

sx = 32.9441

Slope = -0.89075(14.55437)/32.9441 = 0.39352

Question 3: Our least squares regression line associates years as an explanatory variable, with times in the 1,500 meter race as the response variable. Use the least squares regression line you found in question 2 to predict the 1,500 meter time in the 2008 Olympic Games in Beijing. Comment on your prediction.

0.39352 = Time/2008

therefore:

Time = 2008 * 0.39352

= 790.18816