The following table depicts the income and expenditure of 12...

The following table depicts the income and expenditure of 12 randomly chosen families per month and the gender of the head of the family in a certain locality. The value M in gender value is encoded as 1 and F is encoded as 0. Expenditure | Income | Code | Gender 37070 | 45100 | 1 | M 22700 | 28070 | 1 | M 24260 | 26080 | 0 | F 30420 | 35000 | 1 | M 17360 | 18860 | 0 | F 33520 | 41270 | 1 | M 26960 | 32940 | 1 | M 19360 | 21440 | 0 | F 35680 | 44700 | 1 | M 22360 | 24400 | 0 | F 28640 | 33620 | 0 | F 39720 | 46000 | 1 | M

Transcript

00:01 Okay, so i see that you need help with this question.

00:03 And it says, determine the best fitting regression for the above data from income and gender.

00:08 So income and gender.

00:13 What is the value of the coefficient of determination? how do you interpret it? so income and gender.

00:22 So we are going to have, let me just make this bigger.

00:27 Oops.

00:27 Oops, okay, so i have 45100, and that's a male, and then i have 28070, and that's a male, and i have 26080, female, and then i have 35000, male, and then 18860 is female, male.

01:13 41270, and that's a male.

01:16 Then i have 32940, and that's a male.

01:20 Then i have 21440, and that's a female.

01:27 Then i have 44700, 24400, 33620, and 46000.

01:43 So it goes male, male, female.

01:47 I just want to separate these and then next to two one four four zero that's a female and then male female female male okay so it wants the coefficient of determination so okay so in order to find the coefficient of determination determination you have to put these into a table and you have to then so male is one and female is zero okay so then what you have to do is it's terrible straight line you have to find x squared is and then you have to find out what y squared is and then you have to find out what but x times y, okay? and so the sum of x squared is 1, 3, 6, 5, 8, 5, 6, 5, 4, 0, 0.

03:10 And the sum of y squared is 7.

03:13 And the sum of x times x squared is 2, 6, 4, 0, 8, 0.

03:21 Zero.

03:22 So then what you have to do is you have to take this one, three, six, this number of x squared, and you have to subtract it by one 12th because there's 12 numbers and multiply it by the 1 ,500 or not 1 ,000, 1 -5 -0 -9 -1 -6 -7 -1 -0 -4 -0 -0.

03:46 And you're going to get 1 -0 -8 -2 -1 -7 -6 -8 -6 -6 .66 repeating and you are then going to find ssy so you're going to take 7 minus 112 times 49 and you are going to get 2 .916 repeating so then you're going to take um of your 26, 264 ,080, you're going to subtract it by 1 12th and times it by 2 7 1 9 3 6 0.

04:36 And then you are going to get 3 7 6 4 6 6.

04:44 And then you take your sum of your squares of x times y divided by the square root of sum of the squares of x times the sum of the squares of y.

04:53 And you are going to get a correlation coefficient.

04:58 And that is going to be r equals 0 .6669.

05:04 And so your coefficient of determination is when you square this number.

05:10 So you are going going to get 0 .0, 0 point, so r squared equals 0 .66, i'm sorry, not that.

05:31 So r squared equals 0 .4448.

05:36 So i hope that this video helps with that portion.

05:41 Then it wants you to state the explicit hypotenuse at 0 .5 level of significance and interpret the conclusion.

05:51 So it wants you to find a difference or see how they compare between a 90 and a 98 % confidence interval.

06:02 So let's calculate that next...

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