we reject the null hypothesis Ho: B1 B₂ = ... = Bk = 0 for a multiple regression model, that means that there is a linear relationship between y and each of the x variables. Select one: True False
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- In simple linear regression, most often we perform a two-tail test of the population slope 1 to determine whether there is sufficient evidence to infer that a linear relationship exists. The null hypothesis is stated as:We have been assigned to determine how the total weeklyproduction cost for Widgetco depends on the number ofwidgets produced during the week. The following modelhas been proposed:Y b0 b1X b2X2 b3X3 where X number of widgets produced during the weekand Y total production cost for the week. For 15 weeksof data, we found that SSR 215,475 and SST 229,228.For this model, we obtain the following estimated regressionequation (t-statistics for each coefficient are in parentheses):yˆ 29.7 19.8X 0.39X2 0.005X3(0.78) (0.62) (1.25)a For a 0.10, test H0: bi 0 against Ha: bi 0(i 1, 2, 3).b Determine R2 for this model. How can the high R2value be reconciled with the answer to part (a)?The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.7 8.4 6.9 3.4 2.6 2.2 2.2 0.5 yy 14 11.3 9.7 7.1 6.3 5.8 5.6 4.8 xx = thousands of automatic weaponsyy = murders per 100,000 residentsDetermine the regression equation in y = ax + b form and write it below. (Round to 2 decimal places) syntax error: this is not an equation A) How many murders per 100,000 residents can be expected in a state with 8.7 thousand automatic weapons? Answer = Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 6.1 thousand automatic weapons? Answer = Round to 3 decimal places.
- If a linear regression equation had the following form Y = 3 - 2 X: choose the correct statement : Select one: a. The y intercept must be negative b. Sum of squared due to regression must be 0 c. The sample correlation coefficient must be negative o d. The coefficient of determination must be negative 29 36 Next page Fini IYITY NEXT ACTIVITYThe table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.6 8.3 7.1 3.3 2.8 2.7 2.5 0.4 yy 13.9 11.2 9.8 7.1 6.2 6.5 6 4.5 xx = thousands of automatic weaponsyy = murders per 100,000 residentsDetermine the regression equation in y = ax + b form and write it below. __________Round to 2 decimal places A) How many murders per 100,000 residents can be expected in a state with 1.8 thousand automatic weapons? Answer = ______ Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 10.2 thousand automatic weapons? Answer = ______ Round to 3 decimal places.O For the following multiple linear regression model y = Bo + B1x1 + B2x2 + B3x3 + B4x4 + € Derive the test statistic to test Ho : B1 = B2 B3 = B4
- A research company summarized advertising expenditure and sales results as follows: Adv, Exp, |Sales ($) Mean 20 200 S.D. 18 170 Karl Pearson's Correlation Coeff. (r) 0.6 Derive the two regression equations.Use the following table to find the equation of the regression line, between x and y 2 3 4 1 2 3 y 1 2 3 3 2 O ý = 2.97x - 0.455 O ý = -0.455x + 2.97 O ý = 2.122x + 0.098 O ý = 0.098x + 2.122Which of the following four statements is correct?Note: Only one answer is correct per question.1) Let f (x) = 2 + 5x be a linear regression line of a linear regression from Y to X.Then the following applies to the scatter plot: 1) The closer the points in the scatter diagram to the regression line drawnthe stronger the correlation between X and Y. 2) The further the points in the scatter plot are from the regression line drawn away, the stronger the correlation between X and Y. 3) Only if all points lie exactly on the regression line drawn isthe correlation between X and Y is strong. 4) The position of the points in the scatter plot has nothing to do with the strength of the correlation. 2) For the events A = "number of points when rolling the dice is two" and B = "number of points when rolling the diceRolling the dice is straight ":* P (A \ B) is smaller than P (A).* P (A \ B) is the same size as P (A).* P (A \ B) is greater than P (A).* No general statement can be made about…
- Q2. The Update to the Task Force Report on Blood Pressure Control in Children reported the observedaverage SBP in single years of age from age 1 to 17 based on prior studies. The data for boys of averageSBP at each age are given in HW 5 data.sav on Blackboard. Suppose we seek a more efficient way todisplay the data and choose linear regression to accomplish this task.1) Fit a regression line using age as independent variable and SBP as dependent variable. (Theappropriate output is required here if you used software)2) Interpret the regression equation.3) Provide and interpret a 90% confidence interval for the parameters of the regression line.4) Perform ANOVA test for the population slope. Use α = 0.05, and both rejection region and p-value to make a decision.5) What the predicted (estimated) blood pressure on average is for a 10-year-old boy as estimatedfrom the regression line?6) Interpret R2.7) Check the conditions for your regression analysis using the appropriate plots. Age…ASAPA researcher wants to know if there is a significant correlation between hours spent studying for an exam (X) and exam performance (Y). Level of significance is 0.05, degrees of freedom is 3, and the critical value is 0.878. Interpret the strength and direction of the correlation, calculate and interpret the coefficient of determination, then develop the simple regression equation for the two variables. X (Time Spent Studying in Hours) Y (Exam Performance, 0 to 100) 3 56 6 77 7 79 8 70 11 96 Mean 7.00 75.60 SD 2.92 14.54 For this question, on your hand calculation document clearly state: a) the null hypothesis, b) the alternative hypothesis, c) the alpha level you are using, d) the critical value, e) process for calculating r, f) your decision about the null hypothesis, g) the coefficient of determination, h) and regression equation. This is what I will be marking. You may also enter your responses here, but it is…