Quiz_1. Answer. Five models in the image have zero bias.

Quiz_2. Answer. The equation of the green model is y = 0.5x.

Quiz_3. Answer. The equation of the blue model is y = x.

Quiz_4. Answer. The equation of the black model is y = 2x.

Quiz_5. Answer. The equation of the purple model is y = 4x.

Quiz_6. Answer. The equation of the model parallel to the black model is y = 2x + 2.

Quiz_7. Answer. The bias of the model parallel to the black model passing through a point (0, 3 ) is 3; b = 3.

Quiz_8. Answer. The bias of the model parallel to the black model passing through a point (0, 4 ) is 4; b = 4.

|| **corrigenda** ||

There are two typos in my first set of questions, Q#7 and Q#8. They should be (0, 3) and (0, 4) respectively.

I should like to edit them, if possible.

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Explanation and insight:

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We have shown five models going through the Origin, (0, 0) and they are (i) red, (ii) green, (iii) blue, (iv) black, and (v) purple.

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(i) The red line is lying flat coincident with the x-axis. It goes through (0, 0), it means b = 0, it is coincident with the x-axis, it means m = 0. Therefore, the equation of the **red model** is y=0 (y = 0 times x + 0 = 0)

Another way of looking at it is, all y-values on the x-axis is 0, there the equation of the x-axis is 0.

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(ii) The green model has a positive slope. When we are dealing with such a model, y has a positive correlation with x.

As x increases, y increases. If we are asked, at what rate is y increasing with respect to x, immediately we start looking for the slope to answer this question.

What is the slope? The slope is the tangent, the dy/dx, the coefficient (coef_), aka m. What is **m** here; how do we find **m** from the graph? We say, ‘rise over run’. rise is the y-value, run is the x-value? m (== 1/2 == 2/4 == 3/6) from the graph.

((aka == also known as))

Since m=0.5, the green model may be represented by the equation, y = 0.5x (with no bias, as b = 0)

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(iii) The next model is the blue model. Its slope, m is 1. (2/2 == 4/4). So the model may be represented by the equation, y = x (with no bias, as b = 0)

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(iv) The black model is the next model the slope of which is 2 (4/2); 4 is the rise; 2 is the run. So the black model may be represented by the equation, y = 2x (with no bias, as b = 0)

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(v) The fifth model is the purple model the slope of which is 4 (4/1); 4 is the rise; 1 is the run. So the purple model may be represented by the equation, y = 4x (with no bias, as b = 0)

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(vi) The sixth model is the second black model parallel to the first black model. How do we know it is parallel to the first black model? The answer is very simple. Its slope is 2. (4 small squares / 2 small squares) rise is 4 small squares; run is 2 small squares. What is the bias of this model? This is the only model the bias of which is not 0; its bias is 2; bias, b = 2. So what is its equation? We know both m and b; so its equation is y = 2x + 2

NB. It would be a good idea if there is provision for subsequent EDITs. To err is human. There should be room for improvement.