EOC Fast Facts 3

Front

What is the correlation coefficient and what does it indicate?

Back

The correlation coefficient (r) is a statistical measure that describes the strength and direction of a relationship between two variables. It ranges from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation.

Front

What does the slope in a linear regression equation represent?

Back

The slope in a linear regression equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). For example, in the equation y = 1.5x + 12, the slope of 1.5 means that for each additional unit increase in x, y increases by 1.5.

Front

How do you model exponential decay?

Back

Exponential decay can be modeled using the equation y = a(1 - r)^t, where a is the initial amount, r is the decay rate, and t is time. For example, if a substance decays at a rate of 20% per hour, the model would be y = 60(0.8)^t.

Front

What is the difference between linear growth and exponential growth?

Back

Linear growth increases by a constant amount over equal intervals, while exponential growth increases by a percentage of the current value, leading to faster growth over time.

Front

What does a scatterplot showing a linear association look like?

Back

A scatterplot showing a linear association has points that closely follow a straight line, indicating a consistent relationship between the two variables.

Front

What is the formula for linear growth?

Back

The formula for linear growth is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is y = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

Front

What does it mean if a correlation coefficient is close to 0?

Back

If a correlation coefficient is close to 0, it indicates that there is little to no linear relationship between the two variables being analyzed.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept in a linear equation is the value of y when x is 0. It represents the starting point of the relationship on the y-axis.

Front

How can you determine the rate of decay from an exponential decay model?

Back

The rate of decay can be determined from the model y = a(1 - r)^t, where r is the decay rate. For example, if r = 0.2, the substance decays at a rate of 20%.