D1 Linear Correlation

Find the value of the linear correlation coefficient r. The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew​ (in millimeters).

0.196

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

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

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.

Match these values of r with the accompanying​ scatterplots: -0.688, 0.994, 0.331, -0.331, and -0.994

Scatterplot 1= 0.994 Scatterplot 2= 0.331 Scatterplot 3= -0.688 Scatterplot 4= -0.331 Scatterplot 5= -0.994

Refer to the accompanying scatterplot. The four points in the lower left corner are measurements from​ women, and the four points in the upper right corner are from men. Find the linear correlation coefficient using only the four points in the lower left corner​ (for women). Do the four points in the upper right corner have the same correlation coefficient?

The correlation coefficient for the points in the lower left corner is r=0. Yes, because the four points in the upper right corner form the same pattern as the four points in the lower left corner.

For a data set of brain volumes (cm^3​) and IQ scores of twelve males, the linear correlation coefficient is r=0.962. Use the table available below to find the critical values of r. Based on a comparison of the linear correlation coefficient r and the critical​ values, what do you conclude about a linear​ correlation?

The critical values are +/- 0.576 Since the correlation coefficient r is in the right tail above the positive critical value, there is sufficient evidence to support the claim of a linear correlation.

Refer to the accompanying scatterplot. What do you conclude about the possible effect from a single pair of​ values?

The effect from a single pair of values can change the conclusion.

Listed below are the overhead widths​ (in cm) of seals measured from photographs and the weights​ (in kg) of the seals. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the critical values of r using α=0.05.

The linear correlation coefficient is r= 0.922 The critical values are r= +/- .811 n=6

Use the given data set to complete parts​ (a) through​ (c) below.​ (Use α=​0.05.) r= .815 critical value= n11 alpha= .602 Identify the feature of the data that would be missed if part​ was completed without constructing the scatterplot. Choose the correct answer.

The scatterplot reveals a distinct pattern that is not a​ straight-line pattern.

Refer to the accompanying scatterplot. The four points in the lower left corner are measurements from​ women, and the four points in the upper right corner are from men. Based on the preceding​ results, what can be​ concluded? Should the data from women and the data from men be considered​ together, or do they appear to represent two different and distinct populations that should be analyzed​ separately?

There are two different populations that should be considered separately.

Refer to the accompanying scatterplot. The four points in the lower left corner are measurements from​ women, and the four points in the upper right corner are from men. Examine the pattern of the four points in the lower left corner​ (from women)​ only, and subjectively determine whether there appears to be a correlation between x and y for women. Choose the correct answer.

There does not appear to be a linear correlation because the points do not form a line.

Refer to the accompanying scatterplot. The four points in the lower left corner are measurements from​ women, and the four points in the upper right corner are from men. Examine the pattern of the four points in the upper right corner​ (from men)​ only, and subjectively determine whether there appears to be a correlation between x and y for men. Choose the correct answer below.

There does not appear to be a linear correlation because the points do not form a line.

Refer to the accompanying scatterplot. The four points in the lower left corner are measurements from​ women, and the four points in the upper right corner are from men. The linear correlation coefficient using all eight points is r= 0.982. Use α=0.05 n= 8 alpha = 0.707 What does r suggest about the relationship between x and y?

There is sufficient evidence to support the claim of a linear​ correlation, because the correlation coefficient is greater than the critical value.

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.

Refer to the accompanying scatterplot. a. Examine the pattern of all 10 points and subjectively determine whether there appears to be a strong correlation between x and y. Do the data points appear to have a strong linear correlation?

Yes If the points in the scatterplot appear to lie in a straight​ line, then there is a strong correlation between the two variables. Since the points appear to lie in a straight​ line, there is a strong correlation between x and y.

Refer to the accompanying scatterplot. The four points in the lower left corner are measurements from​ women, and the four points in the upper right corner are from men. Find the value of the linear correlation coefficient using all eight points. Use α=0.05.

r = 0.982

Refer to the accompanying scatterplot. b. Find the value of the correlation coefficient r. Is there a linear correlation between x and y? Use alpha= 0.01

r= -0.893 There is a linear correlation between x and y because the correlation coefficient is in the critical region. n= 12 critical value alpha 0.01= .708

Use the given data set to complete parts​ (a) through​ (c) below.​ (Use α=​0.05.) Find the linear correlation​ coefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. critical value= n11 alpha= .602

r= .815 There is sufficient evidence to support the claim of a linear correlation between the two variables. If the absolute value of​ r, denoted exceeds the critical​ value, conclude that there is a linear correlation.​ Otherwise, there is not sufficient evidence to support the conclusion of a linear correlation. r= .815 exceeds the critical value of .602

Refer to the accompanying scatterplot. Remove the point with coordinates ​(2​,10) and find the correlation coefficient r and determine whether there is a linear correlation.

r= 0 There is not a linear correlation between x and y because the correlation coefficient is not in the critical region.

Listed below are the overhead widths​ (in cm) of seals measured from photographs and the weights​ (in kg) of the seals. The linear correlation coefficient is r= 0.922. The critical values at alpha are r= +/- .811 (n=6). Because the absolute value of the linear correlation coefficient is ____________ than the positive critical​ value, there ______ sufficient evidence to support the claim that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals for a significance level of α=0.05.

Because the absolute value of the linear correlation coefficient is greater than the positive critical​ value, there is sufficient evidence to support the claim that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals for a significance level of α=0.05.

Use the given data set to complete parts​ (a) through​ (c) below.​ (Use α=​0.05.) Construct a scatter plot

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