Question

In: Statistics and Probability

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 - Mx Y - My (X - Mx)2 (X - Mx)(Y - My)
-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 (SSX) = 123500
Sum of products (SP) = 64368.5

Regression Equation = ŷ = bX + a

b = SP/SSX = 64368.5/123500 = 0.52

a = MY - bMX = 27.34 - (0.52*95) = -22.18

ŷ = 0.52X - 22.18

orchestra answered 1 year ago
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