For each of the following four plots, indicate whether the sample correlation coefficient is strongly positive (greater than 0.3), weak (between -0.3 and 0.3), or strongly negative (less than -0.3). 0- -2- -4- 7.5- 5.0- 2.5- 0.0- -2.5- Plot A Plot C -2 -3 -5 1.00- 0.75- 0.50- 0.25- 0.00- 0.0000- -0.0025 - -0.0050 - X Plot B Plot D -2 3 -10
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- Listed below are amounts of bills for dinner and the amounts of the tips that were left. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of a = 0.01. If everyone were to tip with the same percentage, what should be the value of r? Bill (dollars) Tip (dollars) 31.80 52.94 85.82 102.16 60.17 111.77 D 5.46 6.07 15.82 15.40 11.15 20.32 Construct a scatterplot. Choose the correct graph below. O A. O B. Oc. D. Q 25- 25- 25 0- 30 0- 30 Bill Amount ($) 0+ 30 Bill Amount (S) 0- 30 Bill Amount (S) 120 120 120 Bill Amount (S) 120 The linear correlation coefficient is r= 0.954 (Round to three decimal places as needed.) Determine the null and alternative hypotheses. Ho: p H,: P (Type integers or decimals. Do not round.) Tip Amount ($) ip Amount ($) Tip Amount ($) Tip Amount ($)The data in the table to the right are based on the results of a survey comparing the commute time of adults to their score on a well-being test. Complete parts (a) through (d) below. LOADING... Click the icon to view the table of critical values of the correlation coefficient. a) Which variable is likely the explanatory variable and which is the response variable? Critical Values for Correlation Coefficient n 3 0.997 4 0.950 5 0.878 6 0.811 7 0.754 8 0.707 9 0.666 10 0.632 11 0.602 12 0.576 13 0.553 14 0.532 15 0.514 16 0.497 17 0.482 18 0.468 19 0.456 20 0.444 21 0.433 22 0.423 23 0.413 24 0.404 25 0.396 26 0.388 27 0.381 28 0.374 29 0.367 30 0.361 n (a) Which variable is likely the explanatory variable and which is the response variable? The explanatory variable is…What is the correlation coefficient (r) for the best data set
- Suppose the correlation coefficient r=0.16 Find:a. The coefficient of determination r2= (round to 3 decimal places)b. The percentage of explained variation = % (round to 1 decimal place)c. The percentage of unexplained variation = % (round to 1 decimal place)Perform rank correlation analysis on the following data set: x y -5 1.9 -4 0.9 -3.25 0.7 -2.55 -0.5 -1.85 -1.2 -0.9 -1.7 5.5511151231258E-17 0.7 0.8 1.5 1.55 1.6 2.35 -0.1 3.3 0.8 4.1 -1.1 5.1 -0.9 5.8 -0.8 6.7 0.7 What is the rank correlation coefficient? (Round to three decimal places.) What is the critical rho value at a 0.01 significance? Do we have correlation? Yes, the rank correlation coefficient is smaller (in absolute value) than the critical rho value. No, the rank correlation coefficient is larger (in absolute value) than the critical rho value. No, the rank correlation coefficient is smaller (in absolute value) than the critical rho value. Yes, the rank correlation coefficient is larger (in absolute value) than the critical rho value.The accompanying table lists the ages of acting award winners matched by the years in which the awards were won. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Should we expect that there would be a correlation? Use a significance level of α=0.05. LOADING... Click the icon to view the ages of the award winners. Construct a scatterplot. Choose the correct graph below. A. 20702070Best Actress (years)Best Actor (years) A scatterplot has a horizontal axis labeled Best Actress in years from 20 to 70 in increments of 5 and a vertical axis labeled Best Actor in years from 20 to 70 in increments of 5. Twelve points are plotted. Eleven of the plotted points follow the pattern of a line rising from left to right passing through the points (24, 38) and (66, 58). An…
- The readout of the correlation is r = 0.8162 with a p-value of 0.0022. What does the scatterplot reveal that is missed from the correlation results?Match the following sample correlation coefficients with the explanation of what that correlation coefficient means. Type the correct letter in each box. 1. r= 1 2. r = -1 3. r=-.15 4. r = .1 A. a weak positive relationship between x and y B. a weak negative relationship between x and y C. a perfect negative relationship between x and y D. a perfect positive relationship between x and yComplete the following instructions:i. Identify the independent and dependent variables.ii. Calculate and interpret the Pearson correlation coefficient r for the paired data. Be sure to indicate if the correlation is positive or negative, and whether it is strong, moderate, or weak, or if there does not appear to be any significant correlation. A researcher for a gasoline retailer examines the relationship between the volume of gasoline purchased in kL(i.e. 1000 L) compared to the price of gasoline (in $/L), over a course of several days, to see if there is a correlation between the data: Amount of Gasoline Purchased Price of Gasoline 2.257 1.079 3.126 1.015 2.793 1.046 4.671 0.973 2.137 1.021 5.916 0.939 2.775 0.995 4.88 0.927 3.162 0.964 7.498 0.899 2.971 0.982 3.596 0.945 1.372 1.129 3.961 1.059 i. Independent Variable: Dependent Variable: ii. Pearson correlation coefficient (r): Round to 3 decimal…
- Fifty-four wild bears were anesthetized, and then their weights and chest sizes were measured and listed in a data set. Results are shown in the accompanying display. Is there sufficient evidence to support Correlation Results the claim that there is a linear correlation between the weights of bears and their chest sizes? When measuring an anesthetized bear, is it easier to measure chest size than weight? If so, does it appear that Correlation coeff, r: 0.959614 a measured chest size can be used to predict the weight? Use a significance level of = 0.05. Critical r: +0.2680855 P-value (two tailed): 0.000 Но: Р H1:P (Type integers or decimals. Do not round.) Identify the correlation coefficient, r. (Round to three decimal places as needed.) Identify the critical value(s). (Round to three decimal places as needed.) O A. There is one critical value at r= . B. There are two critical values at r= ± Is there sufficient evidence to support the claim that there is a linear correlation between…the accompanying table shows the ages (in years) of 11 children and the numbers of words in their vocabulary. Age, x Vocabulary size, y1 32 2603 5904 11005 19006 25003 7305 22002 2504 13006 2400 1. Calculate the sample correlation coefficient r. 2. Describe the type of correlation, if any, and interpret the correlation in the context of the data. 3. Use the table of critical values for the Pearson correlation coefficient to make a conclusion about the correlation coefficient. Let α=0.01.