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Explanation: Independent variables, also known as predictors or explanatory variables, are inputs or factors that are manipulated or observed to understand their effect on the dependent variable (outcome). For example, in a study analyzing the impact of advertising budget (independent variable) on sales revenue (dependent variable), the budget is varied to predict its influence on sales. Understanding independent variables is crucial for building predictive models, determining causality, and analyzing relationships. Proper identification of independent variables ensures the reliability and validity of statistical and machine-learning models. Option A: Variables changing in response to others are dependent, not independent. Option C: Constant variables do not vary and hence do not fit the dynamic nature of independent variables. Option D: Variables representing populations are not necessarily independent variables; they could be metadata. Option E: Independent variables have a measurable impact, contrary to what this option suggests.
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Quantity-I: 'D' can do 55% of work in 44 hours. Find the value of 'Y' if the time taken by him to complete the whole work is 'Y' hours.
Quanti...
Quantity I: A bag contains 5 identical gold coins, and the number of ways in which 'p' coins can be drawn from the bag is 10. D...
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Quantity I : The rate at which the train must run to reduce the time to 30 minutes. A train takes 40 minutes for a journey if it runs at 72 km/hr.
...Quantity I: There are two types of animals in a pet shop. Some are puppies and some are kittens. Each kitten takes 8 biscuits and each puppy takes 11 bi...
Quantity I: The cost price of a watch with a marked price of Rs. 500, which, after being sold at a 50% discount, still results in a profit of 25%.
...What is the population of village A in 2021?
Quantity I: Population of village A in 2020 was 55,000 and it increased by 15% in 2021 over 2020.<...
Quantity I: A bag contains 5 red, 7 blue, and 8 green balls. Two balls are drawn randomly. What is the probability that both balls drawn are green?
...f(a) = a3 - 3a2 + 3a - 4
Quantity l: Determine the value of f(a) when a = 3?
Quantity II: Determine the value ...