choose the function that would require a linear regression fit. a. 𝑦 = 𝑥 𝑎 b. 𝑦 = 𝑒 𝑎𝑥 c. 𝑦 = 𝑎𝑥 + 𝑏 d. 𝑦 = sin(𝑎𝑥) in matlab

To choose the function that would require a linear regression fit, we need to determine if the relationship between the dependent variable (y) and the independent variable (x) can be approximated by a linear equation.

a. 𝑦 = 𝑥 𝑎 This is a linear equation and can be approximated by a linear regression fit as it follows the form 𝑦 = 𝑎𝑥.

b. 𝑦 = 𝑒 𝑎𝑥 This is an exponential equation, not a linear equation. Therefore, it is not suitable for linear regression fit.

c. 𝑦 = 𝑎𝑥 + 𝑏 This is a linear equation and can be approximated by a linear regression fit as it follows the form 𝑦 = 𝑎𝑥 + 𝑏.

d. 𝑦 = sin(𝑎𝑥) This is a sinusoidal equation and not a linear equation. Therefore, it is not suitable for linear regression fit.

In summary, the functions that would require a linear regression fit are a. 𝑦 = 𝑥 𝑎 and c. 𝑦 = 𝑎𝑥 + 𝑏.