Question

A department of transportation's study on driving speed and miles per gallon for midsize automobiles resulted in the following data: Speed (Miles per Hour) 29 50 39 55 30 24 61 25 50 56 Miles per Gallon 28 25 25 22 30 33 21 35 25 25 Compute the sample correlation coefficient (to 2 decimals and enter negative value as negative number). What can you conclude, based on your computation of the sample correlation coefficient? There is a strong negative linear relationship Select the correct interpretation for the sample correlation coefficient. (i) For driving speeds between 24 and 61 miles per hour, higher speeds are associated with higher miles per gallon. (ii) For driving speeds between 24 and 61 miles per hour, higher speeds are associated with lower miles per gallon. (iii) For driving speeds between 24 and 61 miles per hour, lower speeds are associated with lower miles per gallon. (iv) There is no relationship between driving speed and miles per gallon. Choice (ii)

          A department of transportation's study on driving speed and miles per gallon for midsize automobiles resulted in the following data:

Speed (Miles per Hour) 29 50 39 55 30 24 61 25 50 56
Miles per Gallon 28 25 25 22 30 33 21 35 25 25

Compute the sample correlation coefficient (to 2 decimals and enter negative value as negative number).

What can you conclude, based on your computation of the sample correlation coefficient?
There is a strong negative linear relationship

Select the correct interpretation for the sample correlation coefficient.
(i) For driving speeds between 24 and 61 miles per hour, higher speeds are associated with higher miles per gallon.
(ii) For driving speeds between 24 and 61 miles per hour, higher speeds are associated with lower miles per gallon.
(iii) For driving speeds between 24 and 61 miles per hour, lower speeds are associated with lower miles per gallon.
(iv) There is no relationship between driving speed and miles per gallon.

Choice (ii)

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A department of transportation's study on driving speed and miles per gallon for midsize automobiles resulted in the following data:

Speed (Miles per Hour) 29 50 39 55 30 24 61 25 50 56
Miles per Gallon 28 25 25 22 30 33 21 35 25 25

Compute the sample correlation coefficient (to 2 decimals and enter negative value as negative number).

What can you conclude, based on your computation of the sample correlation coefficient?
There is a strong negative linear relationship

Select the correct interpretation for the sample correlation coefficient.
(i) For driving speeds between 24 and 61 miles per hour, higher speeds are associated with higher miles per gallon.
(ii) For driving speeds between 24 and 61 miles per hour, higher speeds are associated with lower miles per gallon.
(iii) For driving speeds between 24 and 61 miles per hour, lower speeds are associated with lower miles per gallon.
(iv) There is no relationship between driving speed and miles per gallon.

Choice (ii)

Added by Sheri Q.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Jon Southam

08/29/2022

Step 1

Given data: Speed (Miles per Hour): 29, 50, 39, 55, 30, 24, 61, 25, 50, 56 Miles per Gallon: 28, 25, 25, 22, 30, 33, 21, 35, 25, 25 Using a calculator or statistical software, we find that the sample correlation coefficient is -0.91. ** Show more…

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A department of transportation's study on driving speed and miles per gallon for midsize automobiles resulted in the following data: Speed (Miles per Hour) 29 50 39 55 30 24 61 25 50 56 Miles per Gallon 28 25 25 22 30 33 21 35 25 25 Compute the sample correlation coefficient (to 2 decimals and enter negative value as negative number) What can you conclude, based on your computation of the sample correlation coefficient? There is a strong negative linear relationship Select the correct interpretation for the sample correlation coefficient: (i) For driving speeds between 24 and 61 miles per hour, higher speeds are associated with higher miles per gallon. (ii) For driving speeds between 24 and 61 miles per hour, higher speeds are associated with lower miles per gallon. (iii) For driving speeds between 24 and 61 miles per hour, lower speeds are associated with lower miles per gallon. (iv) There is no relationship between driving speed and miles per gallon. Choice (ii)

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00:01 Here we have some data from the department of transportation.

00:05 And they're looking at the speed, which is our x variable, and miles per gallon, which is our y variable, our independent and dependent variables respectively.

00:15 And so we're looking at, as the speed changes, how is that affecting the miles per gallon? and we want to compute the sample correlation coefficient.

00:25 And here it is, and this is the way i got it, using this formula.

00:30 There's a few other formulas you can use but this is the one i used and this little symbol the sigma that means the sum and so you just take each x value and y value and you square each of them so this column here is filled with the x squared values 29 squared 50 squared and so on so forth this column here let me number these we'll call this column one column two okay column three is going to be our x squared values column 4 will be at our y squared value.

01:06 So we take each y value, square it.

01:10 And then this column 5, we'll call this our, this is our column 5, this is our xy column.

01:17 So we take each x times the y value, so 29 times 29 is 841.

01:22 Ironically, it's the same as x squared and y squared, but that's just coincidence.

01:28 50 times 25 is 1250, 40 times 25 is 1 ,000, and so on and so forth.

01:33 And then you sum each column.

01:35 And that's what these are.

01:36 So this first column here, this is the, this value here, 416, this is the sum of the x's.

01:45 269, that's the sum of the y's.

01:48 This column here, this is the sum of the x squared.

01:50 So you take all these x squared values, sum them up.

01:52 That's what this is.

01:54 The column four gives us the sum, and that's the sum of the y squared.

01:58 And then this last one is the sum of the x times y is the product of the x and y values.

02:03 And so you substitute them into this formula...

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