Curve fitting (polyfit, fit) in MATLAB - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of polyfit polynomial coefficients

What is the output of the following MATLAB code?

x = [1 2 3 4 5]; y = [2.2 4.8 7.1 8.9 11.3]; p = polyfit(x, y, 1); disp(round(p,1))

MATLAB

x = [1 2 3 4 5];
y = [2.2 4.8 7.1 8.9 11.3];
p = polyfit(x, y, 1);
disp(round(p,1))

A [2.3 0.7]

B [1.8 2.2]

C [2.2 1.8]

D [2.2 0.2]

💡 Hint

Recall polyfit returns coefficients starting with highest degree term.

polyfit fits y = p1*x + p2. The slope is about 2.2 and intercept about 0.2 after rounding.

❓ Predict Output

intermediate

Result of fit with custom model

What is the value of the coefficient 'a' after running this MATLAB code?

x = (1:5)'; y = [2.2 4.8 7.1 8.9 11.3]'; ft = fittype('a*x+b'); f = fit(x,y,ft); disp(round(f.a,1))

MATLAB

x = (1:5)';
y = [2.2 4.8 7.1 8.9 11.3]';
ft = fittype('a*x+b');
f = fit(x,y,ft);
disp(round(f.a,1))

A 4.8

B 1.7

C 2.2

D 0.7

💡 Hint

Coefficient 'a' is the slope in the linear model.

The fit finds a slope close to 2.2 matching the data trend.

❓ Predict Output

advanced

Output of polynomial evaluation after polyfit

What is the output of this MATLAB code?

x = 1:4; y = [1 8 27 64]; p = polyfit(x,y,3); val = polyval(p, 2.5); disp(round(val,1))

MATLAB

x = 1:4;
y = [1 8 27 64];
p = polyfit(x,y,3);
val = polyval(p, 2.5);
disp(round(val,1))

A 15.6

B 14.5

C 16.0

D 15.0

💡 Hint

The data is cubic: y = x^3, so polyval should approximate 2.5^3.

2.5^3 = 15.625, rounded to 15.6 matches option A.

❓ Predict Output

advanced

Error type from incorrect fit model syntax

What error does this MATLAB code produce?

x = (1:3)'; y = [2 4 6]'; ft = fittype('a*x^2 + b'); f = fit(x,y,ft);

MATLAB

x = (1:3)';
y = [2 4 6]';
ft = fittype('a*x^2 + b');
f = fit(x,y,ft);

A Error: Undefined function or variable 'a'

B No error, fit succeeds

C Error: Invalid model expression

D Error: Fit cannot converge

💡 Hint

Check if the model string syntax is valid for fittype.

No error is produced; the expression 'a*x^2 + b' is valid because '^' is supported in fittype model strings.

🧠 Conceptual

expert

Choosing polynomial degree with polyfit

Given noisy data points, which polynomial degree chosen with polyfit is most likely to cause overfitting?

A Degree 10 (very high)

B Degree 2 (quadratic)

C Degree 1 (linear)

D Degree 3 (cubic)

💡 Hint

Higher degree polynomials can fit noise, not just trend.

A very high degree polynomial (like 10) fits noise and causes overfitting, losing generalization.