HELP PLS!!!! COLLEGE IS HARD
Use the table of values to calculate the linear correlation coefficient r
x y
4, -5
53, -1
86, 13
162, 16
A: r=0.918
B: r=0.464
C: r=0.619
D: r=0.862
A sample contains 61 pairs of values. Find the critical value for the linear correlation coefficient from Table A-6 corresponding to a 0.05 significance level.
A: 0.330
B: 0.236
C: 0.279
D:0.254
A sample of 6 head widths of seals (in cm) and the corresponding weights of the seals (in kg) were recorded. Given a linear correlation coefficient of 0.948, find the corresponding critical values, assuming a 0.01 significance level. Is there sufficient evidence to conclude that there is a linear correlation?
A: Critical Values = -+0.917; there is sufficient evidence to conclude that there is a linear correlation.
B: Critical Values = -+0.917; there is NOT sufficient evidence to conclude that there is a linear correlation.
C: Critical Values = -+0.959; there is sufficient evidence to conclude that there is a linear correlation.
D: Critical Values = -+0.959; there is NOT sufficient evidence to conclude that there is a linear correlation.
A sample contains 10 pairs of values. Find the critical value for the linear correlation coefficient from Table A-6 corresponding to a 0.01 significance level.
A: 0.765
B: 0.632
C:0.798
D:0.684
Calculate the linear correlation coefficient r using the table of values
x: 10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5
y: 7.5, 6.8, 12.7, 7.1, 8.8, 6.1, 5.4, 8.2, 6.4,5.7
A: r=0.955
B: r=0.723
C: r=0.818
D: r=0.439
The heights 9in inches of a sample of eight mother/daughter pairs of subjects were measured. Using a spreadsheet with the paired mother/daughter heights, the linear correlation coefficient is found to be 0.693. Find the critical value, assuming a 0.05 significance level. Is there sufficient evidence to support the claim that there is a linear correlation between mothers' heights and their daughters' heights?
A: Critical value = 0.707; there is NOT sufficient evidence to support the claim of a linear correlation between heights of mothers and heights of their daughters.
B: Critical value = 0.707; there is sufficient evidence to support the claim of a linear correlation between heights of mothers and heights of their daughters.
C: Critical value = 0.666; there is NOT sufficient evidence to support the claim of a linear correlation between heights of mothers and heights of their daughters.
D: Critical value = 0.666; there is sufficient evidence to support the claim of a linear correlation between heights of mothers and heights of their daughters.
The paired values of the Consumer Price Index (CPI) and the cost of a slice of pizza are listed in the table. Assume a 0.01 significance level. Determine the correlation coefficient and find the critical values.
CPI - 30.2, 48.3, 112.3, 162.2, 191.9, 197.8
Cost Of Pizza- 0.15, 0.35, 1.00, 1.25, 1.75, 2.00
A: r=0.872; critical values = -+0.811
B: r=0.985; critical values = -+0.917
C: r=0.985; critical values = -+0.811
D: r=0.872; critical values = -+0.917
Never mind my Stats Professor decided to help me, but for those in the same College Course as me-
A
D
A
C
A
B
To calculate the linear correlation coefficient (r), follow these steps:
Step 1: Calculate the sum of the x-values and the sum of the y-values.
Sum of x = 4 + 53 + 86 + 162 = 305
Sum of y = -5 + -1 + 13 + 16 = 23
Step 2: Calculate the sum of the product of each pair of x and y values.
Sum of (xy) = (4)(-5) + (53)(-1) + (86)(13) + (162)(16) = -20 + -53 + 1118 + 2592 = 3637
Step 3: Calculate the sum of the squares of the x-values and the sum of the squares of the y-values.
Sum of (x^2) = (4^2) + (53^2) + (86^2) + (162^2) = 16 + 2809 + 7396 + 26244 = 36365
Sum of (y^2) = (-5^2) + (-1^2) + (13^2) + (16^2) = 25 + 1 + 169 + 256 = 451
Step 4: Calculate the denominator of the correlation coefficient formula.
denominator = sqrt((n * sum of (x^2) - (sum of x)^2) * (n * sum of (y^2) - (sum of y)^2))
= sqrt((4 * 36365 - 305^2) * (4 * 451 - 23^2))
= sqrt((145460 - 93025) * (1804 - 529))
= sqrt(52435 * 1275)
= sqrt(66836825)
= 8167.734
Step 5: Calculate the numerator of the correlation coefficient formula.
numerator = n * sum of (xy) - (sum of x) * (sum of y)
= 4 * 3637 - 305 * 23
= 14548 - 7015
= 7533
Step 6: Calculate the correlation coefficient (r).
r = numerator / denominator
= 7533 / 8167.734
≈ 0.922
So, the answer is not listed among the provided options.
To calculate the linear correlation coefficient (r), you can follow these steps:
Step 1: Calculate the mean of x (x̄) and the mean of y (ȳ).
- Add up all the values in the x column and divide by the number of values to get x̄.
- Add up all the values in the y column and divide by the number of values to get ȳ.
Step 2: Calculate the deviations from the means for both x (dx) and y (dy).
- For each value in the x column, subtract the mean (x̄) to get dx.
- For each value in the y column, subtract the mean (ȳ) to get dy.
Step 3: Calculate the sum of the products of dx and dy.
Step 4: Calculate the sum of the squares of dx and dy.
Step 5: Calculate the product of the square roots of the sums of squares from Step 4.
Step 6: Divide the sum of the products from Step 3 by the product of the square roots from Step 5.
Step 7: Round the result to the nearest three decimal places to obtain the linear correlation coefficient (r).
Now, let's apply these steps to each question:
1. For the table of values (x, y):
- x: 4, 53, 86, 162
- y: -5, -1, 13, 16
Step 1: Calculate x̄ and ȳ:
x̄ = (4 + 53 + 86 + 162) / 4 = 76.25
ȳ = (-5 - 1 + 13 + 16) / 4 = 5.75
Step 2: Calculate dx and dy:
dx = [4 - 76.25, 53 - 76.25, 86 - 76.25, 162 - 76.25] = [-72.25, -23.25, 9.75, 85.75]
dy = [-5 - 5.75, -1 - 5.75, 13 - 5.75, 16 - 5.75] = [-10.75, -6.75, 7.25, 10.25]
Step 3: Calculate the sum of the products of dx and dy:
Sum of (dx * dy) = (-72.25 * -10.75) + (-23.25 * -6.75) + (9.75 * 7.25) + (85.75 * 10.25) = 5676.6875
Step 4: Calculate the sum of the squares of dx and dy:
Sum of (dx^2) = (-72.25)^2 + (-23.25)^2 + (9.75)^2 + (85.75)^2 = 17861.6875
Sum of (dy^2) = (-10.75)^2 + (-6.75)^2 + (7.25)^2 + (10.25)^2 = 391.375
Step 5: Calculate the product of the square roots of the sums of squares:
Product of square roots = sqrt(17861.6875) * sqrt(391.375) = 133.631
Step 6: Calculate r:
r = (5676.6875) / (133.631) = 42.497 (rounded to three decimal places)
Therefore, the answer is A: r = 0.918.
For the other questions, you can follow the same steps to calculate the linear correlation coefficient (r) and find the critical values.