A Calculus Instructor Is Interested in Finding the Strength of a Relationship

question 98

Essay

A calculus instructor is interested in finding the strength of a relationship between the final exam grades of
students enrolled in Calculus I and Calculus II at his college. The data (in percentages)are listed below. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | } \text { Calculus I } & 88 & 78 & 62 & 75 & 95 & 91 & 83 & 86 & 98 \\\hline \text { Calculus II } & 81 & 80 & 55 & 78 & 90 & 90 & 81 & 80 & 100\end{array}$$ a)Graph a scatter plot of the data.
b)Find an equation of the regression line.
c)Determine if there is a significant correlation between the data. Use $\alpha$ = 0.01.
d)Predict a Calculus II exam score for a student who receives an 80 in Calculus I. Is your answer a valid
prediction?

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Definitions:

Conditioned Response

The learned response to a previously neutral stimulus after conditioning, as seen in classical conditioning paradigms.

Conditioned Stimulus

A previously neutral stimulus that, after being associated with an unconditioned stimulus, elicits a conditioned response.

Central Amygdala

A region within the amygdala of the brain involved in processing emotions, particularly fear and anxiety responses.

Conditioning Of Fear

Conditioning of fear is a psychological process where an individual learns to associate a neutral stimulus with a fearful or threatening event, resulting in the expression of fear responses to the previously neutral stimulus.