Question 1 Consider the following six sample observations: Yi 263854 X₁ 1 4 2 5 3 4 1. What is the slope and intercept for the estimated regression of Y on X? 2. Calculate values of the error term and residual given that the true ßo = 0 and 3₁ <= 1.5
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- In a sample of cars reviewed by Motor Trend magazine, the mean horsepower (hp) was 150 hp with a standard deviation of 36 hp. The mean weight (lbs) was 2500 lbs with a standard deviation of 720 lbs. Assume the relationship between weight and horsepower is linear and has a correlation of r = +0.55. What is the slope of the linear regression model predicting weight (y-variable) from horsepower (x-variable)? 9 13 15 11A researcher records age in years (x) and systolic blood pressure (y) for volunteers. They perform a regression analysis was performed, and a portion of the computer output is as follows: ŷ = 4.5+ 14.4x Coefficients (Intercept) x Estimate 4.5 Ho: B₁ = 0 H₁: B₁ > 0 Ho: B₁ = 0 Ha: B₁ <0 14.4 Ho: B₁ = 0 Ha: B₁ #0 Std. Error Test statistic 2.9 4.7 1.55 3.06 P-value Specify the null and the alternative hypotheses that you would use in order to test whether a linear relationship exists between x and y. 0.07 0Listed below are systolic blood pressure measurements (in mm Hg) obtained from the same woman. Find the regression equation, letting the right arm blood pressure be the predictor (x) variable. Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 85 mm Hg. Use a significance level of 0.05 Right Arm 101 100 94 75 Left Arm 174 167 146 144 Click the icon to view the critical values of the Pearson correlation coefficient r The regression equation is (Round to one decimal place as needed.) 76 144 CRITS
- Listed below are the overhead widths (cm) of seals measured from photographs and weights (kg) of the seals. Find the regression equation, letting the overhead width be the predictor (x) variable. Find the best predicted weight of a seal if the overhead width measured from a photograph is 1.8 cm, using the regression equation. Can the prediction be correct? If not, what is wrong? Use a significance level of 0.05. Overhead Width (cm) 7.3 7.4 9.8 9.5 8.8 8.5 Weight (kg) 152 187 286 247 237 231 The regression equation is y =+ (x. (Round the y-intercept to the nearest integer as needed. Round the slope to one decimal place as needed.)8. For the following data: a. Find the regression equation for predicting Y from X. b. Calculate the Pearson correlation for these data. Use r and SS, to compute SS standard error of estimate for the equation. and the residual Y 3 3 6. 9. 8 4 3 7 10 9.The following output comes from regression using the actual HW9 scores and the Final test scores from intro stats one semester. Sample size: 50R (correlation coefficient) = 0.3658R-sq = 0.1338Estimate of error standard deviation: 10.36256Parameter estimates: Parameter Estimate Std. Err. DF T-Stat P-Value Intercept 43.558118 11.1716 48 3.899 0.0003 Slope 0.360048 0.132225 48 2.723 0.009 Assume no assumptions are violated. Form a 87% Confidence interval for how much your final is supposed to increase for each problem done on homework 9.Use 5 decimal places
- 5. For the following set of data: Y 1 10 5 4 4 13 a. Find the regression equation for predicting Y from X. b. Does the regression equation account for a significant portion of the variance in the Y scores? Use a = .05 to evaluate the F-ratio %3D X27 33Listed below are systolic blood pressure measurements (in mm Hg) obtained from the same woman. Find the regression equation, letting the right arm blood pressure be the predictor (x) variable. Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 90 mm Hg. Use a significance level of 0.05. Right Arm 101 100 92 75 75 O Left Arm 174 167 181 149 147 Click the icon to view the critical values of the Pearson correlation coefficient r The regression equation is y = + x. (Round to one decimal place as needed.) Given that the systolic blood pressure in the right arm is 90 mm Hg, the best predicted systolic blood pressure in the left arm is mm Hg. (Round to one decimal place as needed.)A dog food company is interested in how much dog food a dog consumes based off of its weight. The company takes a random sample of dogs and finds that the best regression model to represent the data is as follows: Simple Linear Regression Results: Dependent Variable: Ounces of Food Consumed in a Week Independent Variable: Weight Food Consumed=-32.86 +5.25xWeight Sample Size: 500 R2:0.8129 Estimate of error standard deviation: 7.8563121 Suppose that a dog weighs 43.7 pounds, and typically eats 180 ounces of food per week. How many ounces of food would we predict the dog eats in a week, based on the least squares estimate? Provide your answer accurate to 1 digit past the decimal point. Answer: Suppose another dog weighs 20.1 pounds and consumes 70 ounces of food per week. What is the residual associate to this individual using the least squares estimate? Provide your answer accurate to 1 digit past the decimal point. Answer:
- Do the following plots show 1. Constant variability 2. Nearly normal residuals 3. Independent observations for SLR (conditions for linear regression)4. A runner was tested on a treadmill. During the test, his speed x (in km/h) and his heart rate y were measured. The results are shown in the table. y 122 132 145 161 178 190 x 8 10 12 14 16 18 (a) Test for the significance of regression using the analysis of variance with a = 0.05. Find the P-value for this test. Can you conclude that the model specifies a useful linear relationship between these two variables? (b) Estimate ². (c) Estimate the standard error of the slope and intercept in this model. (d) Test the hypothesis that the increase in the speed of 1 km/h results in the runner's heart rate average increase of 7 points at a = 0.05. Suppose that the alternative hypothesis is that the average increase of the runner's heart rate in this situation does not equal 7 points.The correlation between two variables x and y is –0.6. If we used a regression line to predict y using x, what percent of the variation in y would be explained?