Data Analytics with Python Week 7 NPTEL Assignment Answers 2025

NPTEL Data Analytics with Python Week 7 Assignment Answers 2024

1. The interval estimate of the mean value of y (dependent variable) for a given value of x is defined as?
Options:
a. Prediction interval estimate
b. Confidence interval estimate
c. Average regression
d. X vs Y correlation interval
Answer: b
Explanation: A confidence interval estimate gives a range in which the mean of the dependent variable is expected to lie for a given value of the independent variable, with a certain level of confidence.

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2. Which of the following is called Standard Error?
Options:
a. T-statistic squared
b. Square root of SSE
c. Square root of SST
d. Square root of MSE
Answer: d
Explanation: The standard error is the square root of the Mean Squared Error (MSE), which estimates the standard deviation of the error term.

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3. Which of the following is true about multiple regression model?
Options:
a. It has only one independent variable
b. It has more than one dependent variable
c. It has more than one independent variable
d. It has at least 2 dependent variable
Answer: c
Explanation: A multiple regression model includes more than one independent variable to predict the dependent variable.

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4. In a multiple regression model, the error term ɛ is assumed to
Options:
a. Have a mean of 1
b. Have a variance of 0
c. Have a standard deviation of 1
d. Be normally distributed
Answer: d
Explanation: One of the assumptions of linear regression is that the error term is normally distributed.

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5. For a multiple regression model with 2 independent variables, R² = 0.904 and adjusted R² = 0.88, determine the number of observations (n)
Options:
a. 6
b. 7
c. 9
d. 10
Answer: d
Explanation: The relationship between R² and adjusted R² is influenced by the number of observations. Based on the formula for adjusted R², only n = 10 satisfies the given values.

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6. If the R² value is small for a model with a large number of independent variables, the adjusted coefficient of determination ____________
Options:
a. Must be positive
b. Can be negative
c. Is zero
d. Can’t say
Answer: b
Explanation: Adjusted R² can be negative if the added variables don’t improve the model; it penalizes irrelevant features.

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7. Which one of the statements is true regarding residuals in regression analysis?
Options:
a. Mean of residuals is always 0
b. Mean of residuals is always < 0
c. Mean of residuals is always > 0
d. There is no such rule for residuals
Answer: a
Explanation: In linear regression, the sum of residuals is zero, so their mean is always zero.

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8. In a simple linear regression model (one independent variable), if we increase the input variable by 1 unit, how much will the output variable change?
Options:
a. By 1
b. No change
c. By its slope
d. None of these
Answer: c
Explanation: In simple linear regression, the slope (coefficient) tells us the change in output for a unit change in input.

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9. If a linear regression model has train error = 0, then test error______________
Options:
a. Is also 0
b. Is non-zero
c. Is always equal to train error
d. Cannot comment on Test error
Answer: d
Explanation: A zero training error doesn’t guarantee zero test error. The test error depends on how well the model generalizes.

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10. Which of the following evaluation metrics is used to evaluate a model while modelling a continuous output variable?
Options:
a. AUC-ROC
b. Accuracy
c. Logloss
d. Mean-Squared-Error
Answer: d
Explanation: Mean Squared Error (MSE) is appropriate for regression tasks where the output is continuous.