The table below shows primary school enrollment for a certain country. Here, xx represents the number...

The table below shows primary school enrollment for a certain country. Here, xx represents the number of years after 18201820, and yy represents the enrollment percentage. Use Excel to find the best fit linear regression equation. Round the slope and intercept to two decimal places.

x   y
0   0.1
5   0.1
10   0.1
15   0.2
20   0.2
25   0.3
30   0.4
35   0.5
40   0.6
45   1.1
50   1.5
55   3.0
60   4.5
65   5.5
70   6.1
75   6.8
80   7.0
85   8.0
90   9.3
95   10.7
100   12.4
105   14.1
110   16.6
115   17.5
120   19.7
125   19.4
130   32.7
135   40.9
140   47.6
145   57.8
150   57.0
155   61.7
160   63.2
165   75.0
170   76.5
175   96.0
180   92.0
185   100.0
190   100.0

Provide your answer below:

y = x -

Solutions

Expert Solution

X - M_x	Y - M_y	(X - M_x)²	(X - M_x)(Y - M_y)
-95	-27.2359	9025	2587.4103
-90	-27.2359	8100	2451.2308
-85	-27.2359	7225	2315.0513
-80	-27.1359	6400	2170.8718
-75	-27.1359	5625	2035.1923
-70	-27.0359	4900	1892.5128
-65	-26.9359	4225	1750.8333
-60	-26.8359	3600	1610.1538
-55	-26.7359	3025	1470.4744
-50	-26.2359	2500	1311.7949
-45	-25.8359	2025	1162.6154
-40	-24.3359	1600	973.4359
-35	-22.8359	1225	799.2564
-30	-21.8359	900	655.0769
-25	-21.2359	625	530.8974
-20	-20.5359	400	410.7179
-15	-20.3359	225	305.0385
-10	-19.3359	100	193.359
-5	-18.0359	25	90.1795
0	-16.6359	0	0
5	-14.9359	25	-74.6795
10	-13.2359	100	-132.359
15	-10.7359	225	-161.0385
20	-9.8359	400	-196.7179
25	-7.6359	625	-190.8974
30	-7.9359	900	-238.0769
35	5.3641	1225	187.7436
40	13.5641	1600	542.5641
45	20.2641	2025	911.8846
50	30.4641	2500	1523.2051
55	29.6641	3025	1631.5256
60	34.3641	3600	2061.8462
65	35.8641	4225	2331.1667
70	47.6641	4900	3336.4872
75	49.1641	5625	3687.3077
80	68.6641	6400	5493.1282
85	64.6641	7225	5496.4487
90	72.6641	8100	6539.7692
95	72.6641	9025	6903.0897

		SS: 123500	SP: 64368.5

Sum of X = 3705
Sum of Y = 1066.1
Mean X = 95
Mean Y = 27.3359
Sum of squares (SS_X) = 123500
Sum of products (SP) = 64368.5

Regression Equation = ŷ = bX + a

b = SP/SS_X = 64368.5/123500 = 0.52

a = M_Y - bM_X = 27.34 - (0.52*95) = -22.18

ŷ = 0.52X - 22.18

orchestra answered 1 year ago

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