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The graph and accompanying table shown here display 12 observations of a pair of variables (x, y).

The variables x and y are positively correlated, with a correlation coefficient of r = 0.97.

What is the slope, b, of the least squares regression line, y = a + bx, for these data? Round your answer to the nearest hundredth.

2.04 - 2.05

Q: What is the slope b of the least squares regression line y equals a plus bx for these data?

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Yes, it is.

The line of best fit is found by statistical calculations which this site is too crude for. Look up least squares regression equation if you really wish to follow up. The slope of a graph is the slope of the tangent to the graph curve at the point in question. If the function of the graph is y = f(x) then this is the limit, as dx tends to 0, of [f(x + dx) - f(x)]/dx.

There are many terms used for the purpose: slope, gradient, relationship, regression, correlation, error, scatter; as well as phrases: line of best fit, least squares, maximum likelihood. The question needs to be more specific.

line that measures the slope between dependent and independent variables

It guarantees that the slope and intercept are minimized.

Related questions

Yes, it is.

the negative sign on correlation just means that the slope of the Least Squares Regression Line is negative.

Negative

The slope will be negative.The slope will be negative.The slope will be negative.The slope will be negative.

The line of best fit is found by statistical calculations which this site is too crude for. Look up least squares regression equation if you really wish to follow up. The slope of a graph is the slope of the tangent to the graph curve at the point in question. If the function of the graph is y = f(x) then this is the limit, as dx tends to 0, of [f(x + dx) - f(x)]/dx.

There are many terms used for the purpose: slope, gradient, relationship, regression, correlation, error, scatter; as well as phrases: line of best fit, least squares, maximum likelihood. The question needs to be more specific.

Whenever you are given a series of data points, you make a linear regression by estimating a line that comes as close to running through the points as possible. To maximize the accuracy of this line, it is constructed as a Least Square Regression Line (LSRL for short). The regression is the difference between the actual y value of a data point and the y value predicted by your line, and the LSRL minimizes the sum of all the squares of your regression on the line. A Correlation is a number between -1 and 1 that indicates how well a straight line represents a series of points. A value greater than one means it shows a positive slope; a value less than one, a negative slope. The farther away the correlation is from 0, the less accurately a straight line describes the data.

slope

line that measures the slope between dependent and independent variables

It guarantees that the slope and intercept are minimized.

The strength of the linear relationship between the two variables in the regression equation is the correlation coefficient, r, and is always a value between -1 and 1, inclusive. The regression coefficient is the slope of the line of the regression equation.

The method used to calculated the best straight line through a set of data is called linear regression. It is also called the least squares method. I've included two links. I know the wikipedia link is a bit complicated. The slope and intercept are calculated based on "minimum least squares." If I draw a line through the set if points, for every x value in the data set I will have a y value and a predicted y value (y-hat) based on the straight line. The error (E) is this case is the predicted y minus the actual y. Linear regression finds the slope and intercept of the equation that minimizes the sum of the square of the errors. Mathematically this is stated as: Min z = sum (yi - y-hat)^2 To hand calculate a linear regression line wold take some time. The second link that I've included shows how to calculated this using excel.