perform simple linear regression on these data. Share your regression model and
ID: 3125285 • Letter: P
Question
perform simple linear regression on these data. Share your regression model and describe what each regression coefficient (i.e. Beta 0 and Beta 1) means in the context of the case study.
Years Credit Balance($)
2 2,631
2 2,047
1 3,155
2 3,913
5 2,660
3 3,531
10 2,766
4 3,769
4 4,082
6 3,806
8 4,049
9 4,073
9 2,697
11 2,914
10 4,073
4 4,310
10 4,199
10 4,253
13 3,104
10 4,293
5 4,456
11 4,340
5 4,925
13 3,178
11 4,391
6 4,947
15 3,203
8 4,354
10 4,366
6 5,003
15 3,250
11 4,402
10 4,397
13 4,595
13 4,786
14 4,888
8 5,148
14 5,011
8 5,220
16 3,257
15 5,528
9 5,283
9 5,332
17 3,304
19 5,553
10 5,484
18 3,342
18 3,788
10 5,756
10 5,861
Explanation / Answer
Explanation
We will find an equation of the regression line in 4 steps.
Step 1: Find XY and X2 as it was done in the table below.
Step 2: Find the sum of every column:
X=480 , Y=207673 , XY=2023992 , X2 =5614
Step 3: Use the following equations to find a and b:
Regression Formula :
Regression Equation(y) = a + bx as per problem a means b0 and b means b1
Slope(b) = (NXY - (X)(Y)) / (NX2 - (X)2) = 30.15
Intercept(a) = (Y - b(X)) / N =3864.017
Where,
x and y are the variables. b = The slope of the regression line a = The intercept point of the regression line and the y axis. N = Number of values or elements X = First Score Y = Second Score XY = Sum of the product of first and Second Scores X = Sum of First Scores Y = Sum of Second Scores X2 = Sum of square First Scores
Step 4: Substitute a and b in regression equation formula
y=3864.017 + 30.15x
X Y XY XX 2 2631 5262 4 2 2047 4094 4 1 3155 3155 1 2 3913 7826 4 5 2660 13300 25 3 3531 10593 9 10 2766 27660 100 4 3769 15076 16 4 4082 16328 16 6 3806 22836 36 8 4049 32392 64 9 4073 36657 81 9 2697 24273 81 11 2914 32054 121 10 4073 40730 100 4 4310 17240 16 10 4199 41990 100 10 4253 42530 100 13 3104 40352 169 10 4293 42930 100 5 4456 22280 25 11 4340 47740 121 5 4925 24625 25 13 3178 41314 169 11 4391 48301 121 6 4947 29682 36 15 3203 48045 225 8 4354 34832 64 10 4366 43660 100 6 5003 30018 36 15 3250 48750 225 11 4402 48422 121 10 4397 43970 100 13 4595 59735 169 13 4786 62218 169 14 4888 68432 196 8 5148 41184 64 14 5011 70154 196 8 5220 41760 64 16 3257 52112 256 15 5528 82920 225 9 5283 47547 81 9 5332 47988 81 17 3304 56168 289 19 5553 105507 361 10 5484 54840 100 18 3342 60156 324 18 3788 68184 324 10 5756 57560 100 10 5861 58610 100Related Questions
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