Given the data points (0, 2), (1, 1), find the following: (a) The straight line interpolating this data. (b) The function f(x) = a + be* interpolating this data. Hint: Find a and b so that f(0) = 2, f (1) = 1. %3D
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- The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.6 8.5 7.2 3.6 2.6 2.3 2.1 0.4 yy 13.8 11.4 9.9 7.1 5.9 5.8 5.8 4.7 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation y=0.84x+4.02.y=0.84x+4.02. Use this equation to answer the following;Special Note: I suggest you verify this equation by performing linear regression on your calculator.A) How many murders per 100,000 residents can be expected in a state with 4.9 thousand automatic weapons?Answer = Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 10.3 thousand automatic weapons?Answer = Round to 3 decimal places.The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.3 8.6 7.1 3.3 2.4 2.3 2.4 0.7 yy 13.7 11.1 10.4 6.9 6.4 6.2 6.1 4.9 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation y=0.83x+4.28.y=0.83x+4.28. Use this equation to answer the following;Special Note: I suggest you verify this equation by performing linear regression on your calculator.A) How many murders per 100,000 residents can be expected in a state with 10.7 thousand automatic weapons?Answer = Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 1.6 thousand automatic weapons?Answer = Round to 3 decimal places.The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.3 8.6 7.1 3.3 2.4 2.3 2.4 0.7 yy 13.7 11.1 10.4 6.9 6.4 6.2 6.1 4.9 xx = thousands of…Consider the following variables: Y=daily productivity score (measured in points) X1=0 if undergraduate student,1 if graduate student X2=hours of sleep per night 1. The plot shown below could possibly be the graph of which model? 2. If you want to test whether type of student modifies the association between hours of sleep per night and daily productivity score, which model should you consider and what is the null hypothesis for this test? 3. Suppose you use Model 5 to describe the relationship between type of student, hours of sleep per night, and daily productivity score. You use the method of least squares to obtain: Y = -0.5 + 3 (X1) + 1.5 (X2) + 2.5 (X1)(X2).
- The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.8 8.6 7.1 3.9 2.5 2.6 2.4 0.4 yy 14.3 11.5 9.8 7.6 6.2 6.5 6.4 4.1 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation y=0.86x+4.07.y=0.86x+4.07. Use this equation to answer the following; Special Note: I suggest you verify this equation by performing linear regression on your calculator.A) How many murders per 100,000 residents can be expected in a state with 3 thousand automatic weapons?Answer = Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 4.1 thousand automatic weapons?Answer = Round to 3 decimal places.The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.7 8.4 7 3.8 2.7 2.3 2.5 0.3 yy 14.2 11.4 10.2 7.4 6.3 6.1 6 4 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation ˆy=0.89x+3.89.y^=0.89x+3.89. Use this equation to answer the following;Note: Verify this equation using your calculator.A) How many murders per 100,000 residents can be expected in a state with 2.8 thousand automatic weapons?Answer = Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 8.5 thousand automatic weapons?Answer = Round to 3 decimal places.Given datasets X: x1 (1, 4), x2 (2, 3), x3 (3, 4), and x4 (5, -3), x5 (6, -1), x6 (7, -1) with label y = (- 1, -1, -1, 1, 1, 1) respectively, find analytically hard margin W and bias b so that you will be able to determine linear discriminant function f(X) = WT . X + b. You may need to draw the points and estimate the boundary decision function that may be used to help you to make a very first guess the parameter W and b. Once you found the correct discriminant function f(X) = WT . X + b, test your function to correctly classify x1 (1, 4) and x4 (5, -3). Please thoroughly describe.
- The relationship between sleep hours and overall happiness level on the next day was estimated as below in a linear format. (Happiness level is measured through a five-point scale: 1 = Extremely unhappy, 5 = Extremely happy) Overall happiness level = 0.27 * Sleep hours + 2.34 (The p-value for the coefficient of Sleep hours is 0.02.) Based on this equation, what is the expected happiness level of a person on a certain day, when he slept 7 hours the day before?Consider the following variables: Y=daily productivity score (measured in points) X1=0 if undergraduate student,1 if graduate student X2=hours of sleep per night 1. If you want to test whether type of student modifies the association between hours of sleep per night and daily productivity score, which model (from attached image) should you consider and what is the null hypothesis for this test? A. Use Model 3 and test H0: β2=0 B. Use Model 5 and test H0: β3=0 C. Use Model 5 and test H0: β1=0 D. Use Model 5 and test H0: β2=0 E. Use Model 2 and test H0: β1=0 2. Suppose that you decide to use Model 5 (from pocture attached) to describe the relationship between type of student, hours of sleep per night, and daily productivity score. You use the method of least squares to obtain the following: Y= -0.5 + 3(X1) + 1.5(X2) + 2.5(X1X2) What is the estimated slope relating hours of sleep per night and daily productivity score among undergraduate students? A. 2 B. None of…Determine the best (according to sum-of-squares-measure) curve y = Axb, through the data above. Transformed equation ln(y) = ln(A) + b ln(x) or Y = a + bX.
- Imagine that a professor of psychology has two teaching assistants (TAs) who will help her grade assignments for the duration of the semester. The professor wants to make sure that she and the TAs are well calibrated with one another, so she has all three of them grade the first assignment independently. Because the professor grades every assignment on a curve, she first converts the students’ scores to z-scores for each grader. The following table shows the z-scores for a population of 10 students in her class for each grader. Professor Teaching Assistant #1 Teaching Assistant #2 Student 1 0.70 1.27 1.27 Student 2 0.83 -0.64 -1.55 Student 3 -0.98 0.38 -0.14 Student 4 2.21 0.80 0.92 Student 5 -0.54 -1.34 -1.06 Student 6 0.43 0.10 0.30 Student 7 -1.03 -2.09 -1.50 Student 8 -0.01 0.85 1.14 Student 9 -0.54 0.48 0.57 Student 10 -1.07 0.20 0.04 The professor is going to use the z-scores to calculate the correlation coefficient between her scores…Which of the following is a reason why fixed effect models can't estimate coefficients on variables that do not vary within unit? A, The errors will be homoscedastic. B, The de-meaned variables will not vary. C, We can estimate such a variable with fixed effects. D, Because no fixed effects exists in such a case.Determine the best (according to sum-of-squares-measure) curve y = Aebx , through the data above. Transformed equation ln(y) = ln(A) + bx or Y = a + bx.