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  1. Looking at the first scatter plot, we can deduce that there exists a relationship between the duration of old faithful eruption and time taken until the next eruption. The type of correlation exhibited is a positive one since the scatter plot moves from the left to the far right in an increasing pattern. The relationship is also a strong association because the correlation coefficient (0.765050589) is very close to 1 implying that the strength of the relation is strong. Therefore, the two variables exhibit a strong positive correlation.

  2. From the data given, the slope as 12.84948 and the intercept as 30.06644, we can get our regression line which is of the form Y = B0 + B1 X where B0 is the intercept and B1 are the slopes.

Theregression line will therefore be, Y = 30.06644 + 12.84948X

Topredict the time for duration at 3.40 minutes using the regressionline we have,

Y= 30.0644 + 12.84948(3.40)

Itwill be 73.75

Itis therefore approximately 75 minutes.

  1. Examining the second scatter as well, we can figure out that there is perhaps a correlation between the time taken until the next eruption and duration of the old faithful eruption therein. It is maybe a positive association as the scatter plot tends to be moving from left to far right and in an increasing pattern. Moreover, the strength of the relation is a strong association since the correlation coefficient of 0.7650505886 is close to 1 thereby exhibiting a strong relationship. Therefore, we can wrap up that the two variables depict a strong positive correlation.

  2. To begin with, a response variable is one that measures the outcome of research or study, and it is always treated as being dependent. On the other hand, an explanatory variable is one that attempts perhaps to explain the outcomes observed, and it is always treated as being independent.

Whenyou switch the response variable with an explanatory variable, therewill not be any change in the correlation coefficient since everycorrelation is symmetric. That is, cov(x, y) = cov(y, x). However,the regression coefficients will perhaps be different which are usedin making an estimation.


Szekely.G.J.RizzoBakirov, N.K. (2007). Meaning and testing independence by correlationdistances.