Question

If the following data were linearized using logarithms, what would be the equation of the regression line? Round the slope and y-intercept of the regression line to three decimal places.
x y

2 73

3 77

4 85

5 101

6 133


A. log(y) =-1.706x + 0.064

B. log(y) =-0.064x + 1.706

C. log(y) = 1.706x + 0.064

D. log(y) = 0.064x + 1.706

Answer 1

The regression equation is (d) log(y) = 0.064x + 1.706

How to determine the regression equation?

The table of values is given as:

x   2   3   4   5   6

y   73  77  85  101  133

Calculate the logarithm of the y values.

So, we have:

x          2   3   4   5   6

log(y)   1.86  1.89  1.93  2  2.12

Next, we enter the above values in a regression calculator.

From the calculator, we have the following summary:

• Sum of X = 20
• Sum of Y = 9.8
• Mean X = 4
• Mean Y = 1.96
• Sum of squares (SSX) = 10
• Sum of products (SP) = 0.63

The regression equation is then represented as:

log(y) = bx + a

Where:

b = SP/SSX = 0.64/10 = 0.064

a = MY - bMX = 1.96 - (0.064*4) = 1.706

So, we have:

log(y) = 0.064x + 1.706

Hence, the regression equation is (d) log(y) = 0.064x + 1.706

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