Test 10 Statistics

regression equation

Given a collection of paired sample​ data, the____ y=b0+b1x algebraically describes the relationship between the two​ variables, x and y.

scatterplot

When determining whether there is a correlation between two​ variables, one should use a____to explore the data visually.

residual plot

Is a scatterplot of the​ (x,y) values after each of the​ y-coordinate values has been replaced by the residual value y−y.

If we find that there is a linear correlation between the concentration of carbon dioxide in our atmosphere and the global​ temperature, does that indicate that changes in the concentration of carbon dioxide cause changes in the global​ temperature?

No. The presence of a linear correlation between two variables does not imply that one of the variables is the cause of the other variable.

influential points

Paired sample data may include one or more______which are points that strongly affect the graph of the regression line.

What is the difference between the following two regression​ equations?

The first equation is for sample​ data; the second equation is for a population.

In what sense is the regression line the straight line that​ "best" fits the points in a​ scatterplot?

The regression line has the property that the -sum of squares-of the residuals is the -lowest- possible sum.

Which of the following statements about correlation is​ true?

We say that there is a positive correlation between x and y if the​ x-values increase as the corresponding​ y-values increase.

linear correlation coefficient r

measures the strength of the linear correlation between the paired quantitative​ x- and​ y-values in a sample.

What is a​ residual?

A residual is a value of y−y​, which is the difference between an observed value of y and a predicted value of y.

Which of the following is not equivalent to the other​ three?

Dependent variable

residual

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

correlation

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

outlier

is a point lying far away from the other data points.

Question: B. Using the linear correlation coefficient found in the previous​ step, determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. Choose the correct answer below. C. Identify the feature of the data that would be missed if part​ (b) was completed without constructing the scatterplot. Choose the correct answer below.

Answer: B. There is sufficient evidence to support the claim of a linear correlation between the two variables. C. The scatterplot reveals a distinct pattern that is not a​ straight-line pattern.

Question: B. Using the linear correlation coefficient found in the previous​ step, determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. Choose the correct answer below. C.Identify the feature of the data that would be missed if part​ (b) was completed without constructing the scatterplot. Choose the correct answer below.

Answer: B.There is sufficient evidence to support the claim of a linear correlation between the two variables. C.The scatterplot reveals a perfect​ straight-line pattern, except for the presence of one outlier.

Question: A. Do the data points appear to have a strong linear​ correlation? B.Is there a linear correlation between x and​ y? Use α= 0.01. C.Is there a linear correlation between x and​ y? Use α​= 0.01. D.What do you conclude about the possible effect from a single pair of​ values?

Answer: A. Yes. B.Yes​, because the correlation coefficient is in the critical region. C.No​,because the correlation coefficient is not in the critical region. D.The effect from a single pair of values can change the conclusion.