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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- 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?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?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),
- 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.)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:Using 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.
- 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. -1.59Customers 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 0897In 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
- 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.Students graduating Atlantis University are being administered a test to check their general competence level at the end of the study program. From a random sample of 100 students, 95 passed and 5 failed. We aim to construct a 95% confidence interval for the proportion p of students at Atlantis University who have achieved a satisfactory competence level after their studies. Answer the following questions: (a) The critical z-value for this problem (the z-value to be used) is z = (give the exact value to TWO decimal places N.xx) (b)The middle of the interval is %. (ROUND to the nearest integer) (c) The error margin is % (use one decimal only and give in terms of percentages).In bivariate regression, the regression coefficient will be equal to rXY when: