NPTEL Data Analytics with Python Week 6 Assignment Answers 2024
1. In regression analysis, which of the following is not a required assumption about the error term?
a. The expected value of the error term is one
b. The variance of the error term is the same for all values of X
c. The values of the error term are independent
d. The error term is normally distributed
Answer: a
Explanation: In regression, we assume the expected value of the error term is zero, not one. Other assumptions listed here are valid assumptions for classical linear regression.
2. A regression analysis between sales (Y in $1000) and advertising (X in dollars) resulted in the following equation:
Y = 30,000 + 5X
a. Increase of $5 in advertising is associated with an increase of $5,000 in sales
b. Increase of $1 in advertising is associated with an increase of $5 in sales
c. Increase of $1 in advertising is associated with an increase of $35,000 in sales
d. Increase of $1 in advertising is associated with an increase of $5,000 in sales
Answer: b
Explanation: The coefficient 5 means for every $1 increase in X (advertising), Y (sales in $1000) increases by 5 units, i.e., $5,000. But Y is already in $1000 units, so $1 in advertising increases sales by $5 (not $5,000 in raw terms).
3. In a regression and correlation analysis if R² = 1, then
a. SSE = SST
b. SSE = 1
c. SSR = SSE
d. SSR = SST
Answer: d
Explanation: R² = SSR / SST. If R² = 1, it means all variability in Y is explained by X, i.e., SSR = SST and SSE = 0.
4. SSE (Sum of Squares for Error) can never be
a. Larger than SST
b. Smaller than SST
c. Equal to 1
d. Equal to zero
Answer: a
Explanation: SST = SSR + SSE. Since SSE is a part of SST, it cannot be larger than SST. It can be zero (perfect fit), equal to 1, or smaller than SST.
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5. In question no. 6, when testing the hypothesis of slope, we will:
a. Accept the null hypothesis
b. Reject the null hypothesis
c. Can’t state any conclusion
d. None of the above
Answer: b
Explanation: Since answer 6 is b, it likely indicates a significant result (e.g., t-statistic large, p-value small), so we reject the null hypothesis (typically that slope = 0).
6. In question 6, determine a 95% confidence interval for B1 to test the hypotheses
a. (0.045, 0.138)
b. (0.055, 0.148)
c. (0.065, 0.158)
d. (0.075, 0.138)
Answer: a
Explanation: If option (a) contains values that do not include 0 and aligns with previous calculations, it’s the likely interval. Confidence intervals help verify significance—if 0 is not within the interval, the slope is significant.
7. State TRUE or FALSE –
Statement: The variance of error is same for all values of the independent variable
a. True
b. False
Answer: a
Explanation: This is a basic assumption of homoscedasticity in regression analysis—the error variance should remain constant across all X values.
8. Which of the following is possible for the coefficient of determination (R²)?
a. It can be larger than 1
b. It is less than one
c. It can be less than -1
d. None of these alternatives is correct
Answer: b
Explanation: R² ranges from 0 to 1 in simple regression (0% to 100% variability explained). It can never be greater than 1 or negative.
