The line of regression of y on x is given by `1.63x-y=19.36` and regression equation of x on y is `0.596y -x=11.83`. Estimated value of y when x= 13.5 is

Options

A. 5.3
B. 2.645
C. 3
D. 13.5

Answer

To solve the problem step by step, we will follow the instructions given in the video transcript.

### Step 1: Write the regression equation of y on x.
The regression equation of y on x is given as:
\[ 1.63x - y = 19.36 \]

### Step 2: Rearrange the equation to express y in terms of x.
We can rearrange the equation to isolate y:
\[ y = 1.63x - 19.36 \]

### Step 3: Substitute the value of x.
We need to estimate the value of y when \( x = 13.5 \):
\[ y = 1.63(13.5) - 19.36 \]

### Step 4: Calculate the value of y.
Now, we will perform the calculation:
1. Calculate \( 1.63 \times 13.5 \):
\[ 1.63 \times 13.5 = 22.005 \]
2. Now substitute this value back into the equation:
\[ y = 22.005 - 19.36 \]
\[ y = 2.645 \]

### Final Answer:
The estimated value of y when \( x = 13.5 \) is:
\[ y = 2.645 \]

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