Stats Ch. 10

1. If the computed linear correlation coefficient r lies in the left/right tail beyond the leftmost/rightmost critical value. Or if the |r| exceeds value on table A-6. 2. If the computed linear correlation lies between the two critical values.

1. How do we know that there is a correlation (using r)? 2. How do we know if there is no correlation?

There is a positive linear correlation

If the scatterplot shows a distinct straight-line, or linear, pattern, what can we say? As the x-values increase, the corresponding y-values also increase. ex; r = .851

That the Zx*Zy tend to be positive. If its downhill, its the opposite.

If using z-score and Σ(ZxZy) approximate an uphill line, what does this tell us?

explanatory variable; response variable.

The regression equation expresses a relationship between x (called the __________) and y (_______________).

influential points.

What are outliers and special points called?

1. The value of r is always between -1 and 1 inclusive. -1≤ r ≤ 1 2. If all values of either variable are converted to a different scale, the value of r does not change. 3. The value of r is not affected by the choice of x or y. Interchange all x- and y-values and the value of r will not change. 4. r measures the strength of a linear relationship. It is not designed to measure the strength of a relationship that is not linear. 5. r is very sensitive to outlliers in the sense outlier can dramatically affect its value.

What are the properties of r?

1. The same of paired (x,y) data is a random sample. 2. Visual examination of the scatterplot shows that the points approximate a straight-line pattern. 3. Remove outliers.

What are the requirements for a regression line?

1. The sample of paired (x,y) data is a simple random sample of quantitative data. 2. Visual examination of the scatter plot must confirm that the points approximate a straight-line pattern. 3. Outliers must be removed if they are known to be errors.

What are the requirements that should be satisfied before finding r?

1. To assume that correlation implies causality 2. Another error arises with data based on averages Averages suppress individual variation and may inflate the correlation coefficient. 3. A third error involves the property of linearity. If there is no linear correlation, there might be other correlation that is not linear.

What are the three most common errors made in interpreting correlation results?

To make predictions for the value of one of the variables given some specific value of the other variable.

What can use the regression equation for?

Nonlinear relationship

What can we say about r = -.087

Negative correlation

What can we say about r = -.965 As the x values increase, the y values decrease.

No correlation

What can we say about r = 0? No distinct pattern between x and y.

To measure how points are configured among four quadrants.

What can we use Σ(Zx*Zy) for?

3 sig fig.

What do we round bof1 and bof0 to?

That if increase the x (the length) by 1 cm, the predicted height of the person will increase by 3.22 cm.

What does ^y=80.9 + 3.22x tell us?

It can be slope.

What else can the intercept (from the excel) be?

If the R^2 is 1 or very near 1, its a good fit. If its close to 0 its a poor fit.

What is a good fit for R^2? What isn't a good fit?

Expresses a linear relationship between a response variable y and two or more predictor variables (x1,x2...xk) The general form of a multiple equation obtained from sample data is: ^y = b0 + b1x1 + b2x2 + ....bkxk

What is a multiple regression equation?

A range of values used to estimate a variable.

What is a prediction interval?

Is a scatterplot of the (x,y) values after each of the y-coordinate values has been replaced by the residual value y-^y (where ^y ndeontes the predicted value of y). That is, a residul plot is a graph of the points (x,y-^y)

What is a residual plot?

For a pair of sample x,y values, the residual is the difference between the observed sample value of y and the y value that is predicted by using the regression equation. resi=observed y- predicted y = y-^y

What is a residual?

Data for two variables.

What is bivariate data?

Exists between two variables when there is a correlation and the plotted points of paired data result in a pattern that can be approximated by a straight line.

What is linear correlation?

in a variable, is the amount that it changes when the other variable changes by exactly one unit.

What is marginal change?

The coefficient of determination. It is proportion of the variation in y that is explained by the linear relationship between x and y. r^2 = explained variation/total variaion

What is r^2?

The regression line; regression equation.

What is the best fitting line (10.3) that fits a scatterplot of sample data? And its equation?

1. Should not have any obvious pattern. 2. Should not become wider (or thinner) when viewed from left to right.

What is the criteria for a residual plot?

The prediction interval is used for estimate of a value of a variable. A confidence interval is used for an estimate of a value of a population parameter.

What is the difference between the confidence interval and the prediction interval?

If the sum of the squares of the residuals is the smallest sum possible.

What is the least-squares property?

The number that measures how well paired sample data fit a straight-line pattern when graphed.

What is the linear correlation coefficient r?

Close to 0.

What is the value of Σ(Zx*Zy) if the points follow no linear pattern?

Exists between two variables when the values of one variable are somehow associated with the values of the other variable.

Define correlation.

1. If there computed linear correlation coefficient r lies in the left tail beyond the leftmost critical value or if it lies in the right tail beyond the rightmost critical value, reject Ho and conclude that there is sufficient evidence to support the claim. |r| > crit. value 2. Reject if lies between the two crit. values. |r| ≤ crit. val

How do we know there is a correlation and when to reject Ho?

Take x and x-intercept and add them together.

How do you find ^y?

3

How many decimals do we round r to?