least squares regression line

least squares regression line

Assessment

Flashcard

Mathematics

11th - 12th Grade

Practice Problem

Medium

Created by

Rebecca Prather

Used 3+ times

FREE Resource

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18 questions

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1.

FLASHCARD QUESTION

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.

2.

FLASHCARD QUESTION

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.

3.

FLASHCARD QUESTION

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.

4.

FLASHCARD QUESTION

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.

5.

FLASHCARD QUESTION

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.

6.

FLASHCARD QUESTION

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.

7.

FLASHCARD QUESTION

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.

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