I estimate the following regression that relates an individual's test score (from 0 to 100) to their homework grade (also zero to 100): Test Scorei = ẞo + ß₁ · HW Grade¿ + ɛi I find that the intercept is equal to 50. What is difference in predicted test scores for an individual that scored a 90 on homework vs. an individual that scored 95 on the homework? ○ 0.5 ○ 2.5 Not possible to tell from given information ○ 5
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- An instructor who taught two sections of engineering statistics last term, the first with 25 students and the second with 40, decided to assign a term project. After all projects had been turned in, the instructor randomly ordered them before grading. Consider the first 15 graded projects. (a) What is the probability that exactly 10 of these are from the second section? (Round your answer to four decimal places.) (b) What is the probability that at least 10 of these are from the second section? (Round your answer to four decimal places.) (c) What is the probability that at least 10 of these are from the same section? (Round your answer to four decimal places.) (d) What are the mean value and standard deviation of the number among these 15 that are from the second section? (Round your mean to the nearest whole number and your standard deviation to three decimal places.) mean projectsstandard deviation projects (e) What are the mean value and standard deviation of…I estimate the following regression that relates an individual's test score (from 0 to 100) to their homework grade (also zero to 100): Test Scorei = BoB₁ HW Gradei I find that the intercept is equal to 50. What is difference in predicted test scores for an individual that scored a 90 on homework vs. an individual that scored 95 on the homework?In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where O represents the worst possible life and 10 represents the best possible life. The responses were normally distributed, with a mean of 5.3 and a standard deviation of 1.9. Answer parts (a)-(d) below. (a) Find the probability that a randomly selected study participant's response was loss than 4. The probability that a randomly selected study participant's response was lons than 4 is (Round to four decimal placos as needed.)
- The task is to implement density estimation using the K-NN method. Obtain an iidsample of N ≥ 1 points from a univariate normal (Gaussian) distribution (let us callthe random variable X) centered at 1 and with variance 2. Now, empirically obtain anestimate of the density from the sample points using the K-NN method, for any valueof K, where 1 ≤ K ≤ N. Produce one plot for each of the following cases (each plotshould show the following three items: the N data points (instances or realizations ofX) and the true and estimated densities versus x for a large number – e.g., 1000, 10000– of discrete, linearly-spaced x values): (i) K = N = 1, (ii) K = 2, N = 10, (iii) K = 10,N = 10, (iv) K = 10, N= 1000, (v) K = 100, N= 1000, (vi) K = N = 50,000. Pleaseprovide appropriate axis labels and legends. Thus there should be a total of six figures(plots),I estimate the following regression that relates an individual's test score (from 0 to 100) to their homework grade (also zero to 100): Test Score = BoB₁ HW Gradei I find that the slope coefficient is equal to 0.5. What is difference in predicted test scores for an individual that scored a 90 on homework vs. an individual that scored 95 on the homework?Use Python or Matlab to produce the solution for the following problems. Calculate the probability that individual has at least two violations. Calculate the expected value and variance of number of violations. Suppose an individual with X violations incurs a surcharge of $30X+$50. Calculate the expected amount of the surcharge, and the variance.
- We predict the amount that a car is worth by it's age (in years). We run a linear regression and obtain the following parameter estimates. b0 = 50,000 b1 = -1,500 How much would you predict a car aged 25 years is worth? Answer:For following observations, fit a line y= a+bx by the method of least squares. Estimate the coefficients, assume that the observations are gathered randomly and independent from populations of normal distributions with constant Variance: x 0.34. 1.38. -0.65. 0.68. 1.40 y. 0.27. 1.34. -0.53. 0.35. 1.28 Continue… x -0.88. -0.3. -1.18. 0.5. -1.75 y -0.98. 0.72. -0.81. 0.64. -1.59In the simple linear regression equation ŷ = bo + b₁x, how is b₁ interpreted? it is the change in that occurs with a one-unit change in y O It is the estimated value of ŷ when x = 0 O It is the change in ŷ that occurs when bo increases O it is the change in ŷ that occurs with a one-unit change in
- Customers are used to evaluate preliminary product designs. In the past, 91% of highly successful products received good reviews, 57% of moderately successful products received good reviews, and 15% of poor products received good reviews. In addition, 40% of products have been highty successful, 35% have been moderately successful and 25% have been poor products. Round your answers to four decimal places (e.g. 98.7654). (a) What is the probability that a product attains a good review? (b) If a new design attains a good review, what is the probability that it will be a highly successful product? (c) If a product does not attain a good review, what is the probability that it will be a highly successful product? (a) 5985 (b) 6082 (c) i 0897Using the Gaussian Probability Density function write a function that will calculate the probability that variable x will be in the range µ − ασ < x < µ + ασ, where α is some multiple of the variance.In linear regression, 8 tells us how meaningful the corresponding x is in predicting the output. This means, ...... O if a particular 8-value is very small compared to others, the corresponding x plays a little role in predicting the output. O if a particular 8-value is very large compared to others, the corresponding x plays a little role in predicting the output.