Question

Run a regression analysis on the following bivariate set of data with y as the response variable.

x	y
45.5	48.3
69.1	110.9
64.6	72.7
73.8	124
62.4	57.6
81.7	108.1
79	92.9
84.7	83.1
52.4	63.7
69.1	76.2
41.8	45.1
55.5	28.4
56.4	55.5
60.1	91
101.4	130.7

Verify that the correlation is significant at an α=0.05α=0.05. If the correlation is indeed significant, predict what value (on average) for the explanatory variable will give you a value of 89.5 on the response variable.

What is the predicted explanatory value? =

HOW COULD THIS BE DONE IN THE CALCULATOR ? AND WHAT DOES EACH VALUE REPRESENT?

Answer 1

Solution:

Step 1: Find X.Y and X2 as it was done in the table below. X.Y 2197.65 7663.19 4696.42 9151.2 3594.24 8831.77 7339.1 7038.57 3337.88 5265.42 1885.18 1576.2 3130.2 5469.1 13252.98 48.3 110.9 72.7 124 57.6 108.1 92.9 83.1 63.7 76.2 45.1 28.4 55.5 91 130.7 45.5 69.1 64.6 73.8 62.4 81.7 79 84.7 52.4 69.1 41.8 55.5 56.4 60.1 101.4 2070.25 4774.81 4173.16 5446.44 3893.76 6674.89 6241 7174.09 2745.76 4774.81 1747.24 3080.25 3180.96 3612.01 10281.96 Step 2: Find the sum of every column x2 69871.39 Y 1188.2, X- 997.5 , X.Y-84429.1 Step 3: Use the following equations to find a and b Σ Y . Σ X2ーΣ X . Σ XY 1188.2 . 69871.39-997.5 . 84429.1 15.69871.39 -997.52 ~-22.554 n . ΣΧΥ-ΣΧ, ΣΥ 15 . 84429.1-9975-1188.2 15 69871.39 - (997.5)4 Step 4: Substitute a and b in regression equation formula У一一22.554 + 1.53-т

On putting y = 89.5 in the estimated regression equation, we will get:

89.5 = -1.53 x - 22.554

-1.53 x = 112.054

x = 112.054/-1.53 = -73.24

x = -74.25