In: Statistics and Probability
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 -
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