Five observations taken for two variables follow a develop a...

Five observations taken for two variables follow. (a) Develop a scatter chart with $x$ on the horizontal axis. (b) What does the scatter chart developed in part (a) indicate about the relationship between the two variables? The scatter chart indicates that there is a negative relationship between the two variables. (c) Compute the sample covariance. Based on the sample covariance, what can be said about the relationship between the two variables? There is a strong positive linear relationship between the two variables. There is a strong negative linear relationship between the two variables. There is no relationship between the two variables. There is a positive linear relationship between the two variables, but the strength of this relationship cannot be determined based on the sample covariance. There is a negative linear relationship between the two variables, but the strength of this relationship cannot be determined based on the sample covariance. (d) Compute the sample correlation coefficient. (Round your answer to three decimal places.)

Transcript

00:01 In this question, there are given two sets of data here for the x values and for the y values.

00:06 So what we have to do, we have to find the sample covariance.

00:11 So the sample covariance, which is denoted by this as x, y.

00:20 So the formula is one.

00:21 This is the sum of xi minus x bar.

00:25 And multiplied by, this is the sum of y minus y bar.

00:29 And this is divided by since it's a sample, we have to just, divide n minus 1 here so what we need we need on the x bar here so for the x bar which is the mean score right and for the mean score we have to add the x values and divide by the number of term so this is equal to three plus six 12 4 and 15 and this is divided by 2 4 5 which is equal to this is 21 40 which is equal to 8 and the next step, we have to just subtract the number from this one here.

01:09 So when we just take the difference, this is xi minus x bar, which is equal to.

01:15 So this is 3 minus 8, which is negative 5, 6 minus 8, this is negative 2, and this is 4, and this is again, negative 4, and this is 7.

01:30 Great, we got these values.

01:32 And also the mean value for the y which is denoted by y bar this is 50 plus 50 plus 40 plus 50 plus 50 plus 30 and divided by there are five numbers here 150 and 250 so this is 220 divided by 5 let me check again yes 220 divided by 4 which is 44 so the y i minus y bar this is equal to 50 minus 50 44 which is 6 and this is also 6.

02:06 This is negative 4.

02:08 And this is 6.

02:09 And this is negative 14.

02:11 So we got these values here.

02:13 So the next step, the covariance here, which is equal to the sum of all these values.

02:19 Let me just add these values together.

02:21 So we have negative 7, 7, and which is equal to, i think this is this here.

02:29 Sorry, we, i mean, this is, so i just make some, i have to just make some correction.

02:34 For the formula.

02:36 This is equal to y -i -minus -y -bar.

02:38 Sorry, my bad.

02:40 So we just multiply them.