Statistics Chapter 10

Which of the following is NOT a property of the linear correlation coefficient​ r? A.)The value of r is always between minus−1 and 1 inclusive. B.)The linear correlation coefficient r is robust. That​ is, a single outlier will not affect the value of r. C.)The value of r is not affected by the choice of x or y. D.)The value of r measures the strength of a linear relationship.

B.)The linear correlation coefficient r is robust. That​ is, a single outlier will not affect the value of r.

The heights​ (in inches) and pulse rates​ (in beats per​ minute) for a sample of 1919 women were measured. Using technology with the paired​ height/pulse data, the linear correlation coefficient is found to be 0.501 Is there sufficient evidence to support the claim that there is a linear correlation between the heights and pulse rates of​ women? Use a significance level of α=0.05

Because l 0.501 l GREATER than the critical value, there IS sufficient evidence to support the claim that there is a linear correlation between the heights and pulse rates of women for a significance level of α=0.05.

The heights​ (in inches) and pulse rates​ (in beats per​ minute) for a sample of 55 women were measured. Using technology with the paired​ height/pulse data, the linear correlation coefficient is found to be 0.923. Is there sufficient evidence to support the claim that there is a linear correlation between the heights and pulse rates of​ women? Use a significance level of α=0.01

Because l 0.923 l is LESS than the critical​ value, there IS NOT sufficient evidence to support the claim that there is a linear correlation between the heights and pulse rates of women for a significance level of α=0.01

Which of the following is NOT a requirement in determining whether there is a linear correlation between two​ variables? A.)A scatterplot should visually show a​ straight-line pattern. B.)Any outliers must be removed if they are known to be errors. C.)If r >​1, then there is a positive linear correlation.Your answer is correct. D.)The sample of paired data is a simple random sample of quantitative data.

C.)If r >​1, then there is a positive linear correlation.Your answer is correct.

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

Correlation

Which of the following is NOT one of the three common errors involving​ correlation? A.)The conclusion that correlation implies causality B.)Mistaking no linear correlation with no correlation C.)The use of data based on averages D.)Correlation does not imply causality

D.)Correlation does not imply causality

Which of the following statements about correlation is​ true? A.)We say that there is a positive correlation between x and y if there is no distinct pattern in the scatterplot. B.)We say that there is a positive correlation between x and y if the​ x-values increase as the corresponding​ y-values decrease. C.)We say that there is a negative correlation between x and y if the​ x-values increase as the corresponding​ y-values increase. D.)We say that there is a positive correlation between x and y if the​ x-values increase as the corresponding​ y-values increase.

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

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

Dependent Variable

Paired sample data may include one or more​ ___________, which are points that strongly affect the graph of the regression line

Influential Points

A straight line satisfies the​ __________________ if the sum of the squares of the residuals is the smallest sum possible.

Least-squares Property

In working with two variables related by a regression​ equation, the​ _________________ in a variable is the amount that it changes when the other variable changes by exactly one unit.

Marginal Change

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.

In a​ scatterplot, a(n)​ ______________ is a point lying far away from the other data points

Outlier

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

Regression Equation

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.

Residual

A​ ______________ is a scatterplot of the​ (x,y) values after each of the​ y-coordinate values has been replaced by the residual value y-y

Residual Plot

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

Scatterplot

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

The linear correlation coefficient r

Which of the following is not a requirement for regression​ analysis?

The method for regression analysis line is not robust. It is seriously affected by a small departure from a normal distribution.

When making predictions based on regression​ lines, which of the following is not listed as a​ consideration?

Use the regression line for predictions only if the data go far beyond the scope of the available sample data.

Which of the following is NOT true for a hypothesis test for​ correlation? A.) If​|r|>critical value, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation.Your answer is correct. B.) If l r l ≤critical value, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation. C.) If the​ P-value is less than or equal to the significance​ level, we should reject the null hypothesis and conclude that there is sufficient evidence to support the claim of a linear correlation. D.) If the​ P-value is greater than the significance​ level, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation.

A.) If ​|r|>critical value, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation.

For a sample of eight​ bears, researchers measured the distances around the​ bears' chests and weighed the bears. Minitab was used to find that the value of the linear correlation coefficient is r =0.996 Using α=​0.05, determine if there is a linear correlation between chest size and weight. What proportion of the variation in weight can be explained by the linear relationship between weight and chest​ size? Critical Values for the Coefficient n a=0.05 a=0.01 4 0.950 0.990 5 0.878 0.959 6 0.811 0.917 7 0.754 0.875 8 0.707 0.834 9 0.666 0.798 10 0.632 0.765 11 0.602 0.735 12 0.576 0.708 13 0.553 0.684 14 0.532 0.661 15 0.514 0.641 16 0.497 0.623 17 0.482 0.606 18 0.468 0.590 19 0.456 0.575 20 0.444 0.561 25 0.396 0.505 30 0.361 0.463 35 0.335 0.430 40 0.312 0.402 45 0.294 0.378 50 0.279 0.361 60 0.254 0.330 70 0.236 0.305 80 0.220 0.286 90 0.207 0.269 100 0.196 0.256 NOTE: To test Ho:p=0, against H1:p# 0, reject Ho if the absolute value of r is greater than the critical value in thee table.

A.)Yes, because the absolute value of the test statistic exceeds the critical value of 0.707. B.)What proportion of the variation in weight can be explained by the linear relationship between weight and chest size? 0.996 squared = 0.992 Therefore, 99.2​% of the variation in weight can be explained by the linear relationship between weight and chest size.