least squares regression line

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

• plug in a predicted guess for y-hat and simplify

• look at the scatterplot

• rearrange the equation to solve for x

• 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.

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

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.

The scatter plot below shows the number of books read by students in Mrs. Hall’s English class and their final grades. Which statement represents the best description about the line of best fit? 

• The more books students read, the lower their English grade.

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

• The fewer books students read, the higher their English grade. 

• No relationship exists between the number of books students read and their English grades. 

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.

What type of association does this graph have?

• positive 

• negative

• none

• all of the above

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'.

What type of association does this graph show?

• Positive

• negative

• none

• all of the above

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'.

Estimate the correlation coefficient.

• r = -0.8

• r = -0.5

• r = 0.5

• r = 0.8

Answer explanation

The correlation coefficient r = 0.8 indicates a strong positive relationship between the variables. This suggests that as one variable increases, the other tends to also increase, making r = 0.8 the correct choice.

In a scatterplot r is called

• Coefficient of Determination

• Correlation coefficient

• Regression Line

• Slope

Answer explanation

In a scatterplot, 'r' represents the correlation coefficient, which measures the strength and direction of a linear relationship between two variables. It is not the coefficient of determination, regression line, or slope.

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

• good

• bad

• ugly

• mean

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.

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

• As x increases, y decreases

• As x increases, y increases

• As x decreases, 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.

What is the primary purpose of a line of best fit in a scatter plot?

• To connect all the data points.

• To show the exact values of the data points.

• To summarize the trend of the data.

• To highlight the outliers in the data.

Answer explanation

The primary purpose of a line of best fit in a scatter plot is to summarize the trend of the data, providing a visual representation of the relationship between the variables rather than connecting all points or showing exact values.