I am unsure how to solve the following problem: Interest rates for home mortgages have, in general, declined during recent months. With the apparent favorable influence for new-home building, there seems to be a clear relationship between x = the prevailing mortgage interest rates and y = the number of new houses being built per month in a Midwestern city over a period of 18 months. A scatterplot of the data collected shows that the linear model is appropriate. The equation of the least-squares regression line isNumber of new houses = 672.89 – 30.65 × Interest rate and r 2 = 0.49.Which of the following descriptions below best represents the value of the slope? The answer is: When the interest rate increases by 1%, the number of new houses being built is expected to drop by 30.65. However, I do not know why this is the correct answer. Can you please explain?

I am unsure how to solve the following problem: Interest rates for home mortgages have, in general, declined during recent months. With the apparent favorable influence for new-home building, there seems to be a clear relationship between x = the prevailing mortgage interest rates and y = the number of new houses being built per month in a Midwestern city over a period of 18 months. A scatterplot of the data collected shows that the linear model is appropriate. The equation of the least-squares regression line isNumber of new houses = 672.89 – 30.65 × Interest rate and r 2 = 0.49.Which of the following descriptions below best represents the value of the slope? The answer is: When the interest rate increases by 1%, the number of new houses being built is expected to drop by 30.65. However, I do not know why this is the correct answer. Can you please explain?

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter4: Linear Functions

Section: Chapter Questions

Problem 8PT: Does Table 1 represent a linear function? If so, finda linear equation that models the data.

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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

I am unsure how to solve the following problem:

Interest rates for home mortgages have, in general, declined during recent months. With the apparent favorable influence for new-home building, there seems to be a clear relationship between x = the prevailing mortgage interest rates and y = the number of new houses being built per month in a Midwestern city over a period of 18 months. A scatterplot of the data collected shows that the linear model is appropriate. The equation of the least-squares regression line is
Number of new houses = 672.89 – 30.65 × Interest rate and r² = 0.49.

Which of the following descriptions below best represents the value of the slope?

The answer is:

When the interest rate increases by 1%, the number of new houses being built is expected to drop by 30.65.

However, I do not know why this is the correct answer.

Can you please explain?

Definition Definition Representation of the direction and degree of correlation in graphical form. The grouping of points that are plotted makes it a scatter diagram. A line can be drawn showing the relationship based on the direction of points and their distance from each other.

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