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In a Simple Linear Regression Problem, the Following Statistics Are (xxˉ)(yyˉ)\sum ( x - \bar { x } ) ( y - \bar { y } )

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In a simple linear regression problem, the following statistics are calculated from a sample of 10 observations: (xxˉ) (yyˉ) \sum ( x - \bar { x } ) ( y - \bar { y } ) = 2250, SxS _ { x } = 10, x\sum x = 50, y\sum y = 75 The least squares estimates of the slope and y-intercept are respectively:

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Definitions:

Alternative Hypothesis

A statement that contradicts the null hypothesis and indicates there is an effect or difference.

Critical Value Approach

A method used in hypothesis testing where the value of the test statistic is compared to a critical value to decide whether to reject the null hypothesis.

Hypothesized Population

The theoretical or assumed characteristics of a population from which a sample is drawn for the purpose of hypothesis testing.

Standard Error

A statistical measure that describes the accuracy with which a sample distribution represents a population by quantifying the dispersion of sample means around the population mean.

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