According to the nutrition research, recommendation on the consumption of fiber for children and teenagers is the following (y is the amount of fiber per day (in grams), x is the age): y 20 22 26 29 31 33 37 40 41 4 6 8 10 12 14 16 18 X (a) Test for the significance of regression using the analysis of variance with a = 0.05. Can you conclude that the model specifies a useful linear relationship between these two variables? We (b) Estimate ². Round your answer to three decimal places (e.g. 98.765). = ✓conclude that the model specifies a useful linear relationship at a = 0.05. (c) Estimate the standard error of the slope and intercept in this model. Round your answers to three decimal places (e.g. 98.765). se(3₁) = se(Bo) = i i

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 11

c) Show that the coefficient of determination, R², can also be obtained as the squared correlation between actual Y values and the Y values estimated from the regression model where Y is the dependent variable. Note that the coefficient of correlation between Y and X is Eyixi r = And also that ỹ = ŷ (18.75)

Do movies of different types have different rates of return on their budgets? Here's a regression of USGross (SM) on Budget for comedies and action movies with an indicator variable. Complete parts (a) through (d). Dependent variable is: USGross ($M) Coefficient SE(Coeff) - 6.78278 16.95 1.00523 Variable Constant Budget ($M) Comedy 24.0373 0.1613 11.73 t-ratio P-value -0.400 0.6907 6.23 <0.0001 2.05 0.0451 a) Write out the regression model. USGross = + ( Budget + (Comedy R-squared = 32.8% R-squared (adjusted) = 31.0% s = 47.51 55 degrees of freedom

The table below gives the number of weeks of gestation and the birth weight (in pounds) for a sample of five randomly selected babies. Using this data, consider the equation of the regression line, y = bo + b1x, for predicting the birth weight of a baby based on the number of weeks of gestation. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Weeks of Gestation 33 34 36 38 41 Weight (in pounds) 6 6.1 6.8 7.3 7.9 Table Copy Data Step 4 of 6: Find the estimated value of y when x = 36. Round your answer to three decimal places.

Are the years of education of a child dependent on the years of education of their parent? The table shows the number of years of education of parent and the number of years of education of their child.   Years of Education of Parent 13 9 7 12 12 10 11 Years of Education of their Child 13 11 7 16 17 9 17   If there is a significant linear correlation between the variables, determine the regression equation. Are the years of education of a child dependent on the years of education of their parent? The table shows the number of years of education of parent and the number of years of education of their child.   Years of Education of Parent 13 9 7 12 12 10 11 Years of Education of their Child 13 11 7 16 17 9 17   If there is a significant linear correlation between the variables, determine the regression equation. y’ = 1.5x - 3 There is no significant correlation between the variables,…

The following data shows memory scores collected from adults of different ages. Age (X) Memory Score (Y) 25 10 32           10 39 9 48 9 56 7 Use the data to find the regression equation for predicting memory scores from age. The regression equation is: Ŷ = 4.33X + 0.11 Ŷ = -0.11X + 4.33 Ŷ = -0.11X + 13.26 Ŷ = -0.09X + 5.4 Ŷ = -0.09X + 12.6   Use the regression equation you found in question 6 to find the predicted memory scores for the following age: 28 For the calculations, leave two places after the decimal point and do not round:   Use the regression equation you found in question 6 to find the predicted memory scores for the following age: 43 For the calculations, leave two places after the decimal point and do not round:   Use the regression equation you found in question 6 to find the predicted memory scores for the following age: 50 For the calculations, leave two places after the decimal point and do not round:

A draft research report shows the following descriptive statistics on the relationship between blood pressure and height for a large representative sample of American men: average height 70 inches average blood presssure 124 mm correlation between height and blood pressure - 0.2 It also shows the following regression equation for predicting blood pressure from height: predicted blood pressure = (-0.9 mm per inch) × height + 163 mm Is there anything evidently wrong with these results? Choose one option, and briefly explain your answer below. i. There may be something wrong, but there is not enough information here to decide. ii. Something is definitely wrong. Answer: ? ✓ Explain: