least squares regression line

Front

Y-hat is the ________ value of y for a given value of x.

Back

predicted

Answer explanation

Y-hat (\u02C6y) represents the predicted value of y for a given value of x in regression analysis. It indicates the expected outcome based on the model, making 'predicted' the correct choice.

Front

What is the formula for the regression line?

Back

Answer explanation

The correct formula for the regression line is \(\hat{y} = a + bx\). This represents the predicted value of y based on the linear relationship with x, where a is the y-intercept and b is the slope.

Front

_____________________ is the use of a regression line for prediction outside the interval of x values used to obtain the line.

Back

Extrapolation

Answer explanation

Extrapolation is the correct term for using a regression line to make predictions beyond the range of the original x values. It involves estimating values outside the observed data interval.

Front

To make a prediction using the regression line, you would...

Back

plug in a value for x and simplify

Answer explanation

To make a prediction using the regression line, you plug in a value for x into the regression equation and simplify to find the predicted value of y (y-hat). This is the correct method for making predictions.

Front

A ______________ regression line makes the residuals as small as possible.

Back

good

Answer explanation

A good regression line minimizes the residuals, which are the differences between observed and predicted values. This means it fits the data well, making 'good' the correct choice.

Front

You are analyzing a scatter plot that has a negative correlation. What is true of the x and y values?

Back

As x increases, y decreases

Answer explanation

In a scatter plot with a negative correlation, as x increases, y decreases. This means that higher values of x correspond to lower values of y, confirming the correct choice.

Front

What type of correlation describes the relationship between the temperature outside and the number of hot chocolates sold at a football game?

Back

negative

Answer explanation

The correlation is negative because as the temperature increases, the sales of hot chocolate typically decrease. People are less likely to buy hot chocolate when it's warm outside.

Front

The scatter plot shows the number of books read by students in Mrs. Hall’s English class and their final grades. What does the line of best fit indicate?

Back

The more books students read, the higher their English grade.

Answer explanation

The scatter plot indicates a positive correlation between the number of books read and final grades. Therefore, the correct statement is: The more books students read, the higher their English grade.

Front

What type of association does this graph have?

Back

negative

Answer explanation

The graph shows a negative association, meaning that as one variable increases, the other decreases. This is evident from the downward trend in the data points, confirming the correct choice is 'negative'.

Front

What type of association does this graph show?

Back

none

Answer explanation

The graph shows no clear trend or relationship between the variables, indicating that there is no association. Therefore, the correct answer is 'none'.