Assignment7-320-MultipleRegression2

Mental development in humans is related to the volume of the part of the brain known as the hippocampus. The given regression output shows the mental development index at age 24 months vs. the hippocampus volume in ml at birth for a representative sample of 17 premature infants. MDI_24 By Vol(ml) 2.5 2.4- 2.3- 2.2- 2.1- 2- 1.9- 1.8- 1.7- 1.6- 1.5- 50 60 70 80 90 100 110 12 Vol(ml) Regression Analysis MDI_24MO = 1.1359094 + 0.0093475*HippoVol Summary of Fit RSquare RSquare Adj S Mean of Response 0.265 0.216 0.223 1.97758 NObservations 17 Analysis of Variance Source Model DF Sum of Squares 1 0.268 Mean Square F Ratio 0.268 5.4023 MDI_24M0

Define regression line

Find the slope of regression line, y-intercept of regression line, coefficient of determination (r^2), and the linear correlation coefficient (r)

A regression was run to determine if there is a relationship between the happiness index (y) and lifeexpectancy in years of a given country (x). The results of the regression were: y^=a+bx ; a=-0.423 ,b=0.07 a. Write the equation of the Least Squares Regression line.b. Find the value for the correlation coefficient, r?c. If a country increases its life expectancy, the happiness index will Increase or decrease ( circleone)d. If the life expectancy is increased by 1 year in a certain country, how much will the happinessindex change? Round to two decimal places.e. Use the regression line to predict the happiness index of a country with a life expectancy of 85years. Round to two decimal places.-

Describe about how to place a regression line?

Using SAS, draw a scatterplot between variables CRIME_RATE and PROP_CHANGE_INCOME. Attach the scatterplot. Are those two variables good candidates to be analyzed using linear regression? Explain why or why not. crime_rate 150 100 50 O 15 O O 20 O O O 25 O 8 O O 8 O O o O prop_change_income O O O 30 O O O 35 O O O 40

Compute the least-squares regression line for predicting y from x given the following summary statistics. Round the slope and y-intercept to at least four decimal places. x = 12.5 sx = 2.2 y = 1400 sy = 1.8 r = 0.50         Regression line equation: y^ = ___. image attached bellow for better view.

Use the least squares regression line of this data set to predict a value. Meteorologists in a seaside town wanted to understand how their annual rainfall is affected by the temperature of coastal waters. For the past few years, they monitored the average temperature of coastal waters (in Celsius), x, as well as the annual rainfall (in millimetres), y. Rainfall statistics • The mean of the x-values is 11.503. • The mean of the y-values is 366.637. • The sample standard deviation of the x-values is 4.900. • The sample standard deviation of the y-values is 44.387. • The correlation coefficient of the data set is 0.896. The least squares regression line of this data set is: y = 8.116x + 273.273 How much rainfall does this line predict in a year if the average temperature of coastal waters is 15 degrees Celsius? Round your answer to the nearest integer. millimetres

For a regression line y^=mx+b, what does the Sum of Squares Due to Error measure? Select the correct answer below: the total variation in x that cannot be explained by variation in y the total variation in y that cannot be explained by the error, or residuals, for x the total variation in y that cannot be explained by the variation in x the total variation in x that cannot be explained by the error, or residuals, for y

how to perform a linear regression to test the relationship between an independent and dependent variable where the data consists of 5 groups with repeated measures?

Study conductes in patients with HIV. Primary outcome is CD4 coubt(measure stage of disease). Lower CD4=more advanced disease. Wqnt to find association between taking vitamins and supplements and CD4 count. Multiple regression analysis done relating CD4 to use of supplements (1=yes 0=no) and to duration of HIV in years. (# of yeara between diagnosis and study date) y=CD4 Count Y=501.41+12.67 supplements -30 23 duration of HIV.  A. What is ezpected CD4 count for patients taking supplements who had HIv for 2.5 years? B. Expected CD4 count not takong supplements with HIv at study start date? C. Expected CD4 coubt for patients not taking supplements with HIV for 2.5 years? D. Uf compare 2 patients, 1 HIV for 5 years longer than other, whats expected difference in CD4 count?

please anwer whatever you are allowed too. Thank you. A regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).The results of the regression were: ˆyy^=a+bxa=-1.68b=0.168 (a) Write the equation of the Least Squares Regression line of the formˆyy^= + x(b) Which is a possible value for the correlation coefficient, rr? -1.417 1.417 0.702 -0.702 (c) If a country increases its life expectancy, the happiness index will increase decrease (d) If the life expectancy is increased by 0.5 years in a certain country, how much will the happiness index change? Round to two decimal places.(e) Use the regression line to predict the happiness index of a country with a life expectancy of 69 years. Round to two decimal places.

Pre-study scores versus post-study scores for a class of 120 college freshman English students were considered. The residual plot for the least squares regression line showed no pattern. The least squares regression line was \hat{y} = 0.2 + 0.9xy^​=0.2+0.9x with a correlation coefficient r = 0.76. What percent of the variation of post-study scores can be explained by the variation in pre-study scores? 57.8% 87.2% 52.0% 76.0% We cannot determine the answer using the information given.

Interpret the least squares regression line of this data set. Meteorologists in a seaside town wanted to understand how their annual rainfall is affected by the temperature of coastal waters. For the past few years, they monitored the average temperature of coastal waters (in Celsius), x, as well as the annual rainfall (in millimetres), y. Rainfall statistics • The mean of the x-values is 11.503. • The mean of the y-values is 366.637. • The sample standard deviation of the x-values is 4.900. • The sample standard deviation of the y-values is 44.387. • The correlation coefficient of the data set is 0.896. The correct least squares regression line for the data set is: y = 8.116x + 273.273 Use it to complete the following sentence: The least squares regression line predicts an additional annual rainfall if the average temperature of coastal waters increases by one degree millimetres of Celsius.

Please answer all parts of the question, thank you

Managers rate employees according to job performance and attitude. The results for several randomly selected employees are given below. Performance 59 63 65 69 58 77 76 69 70 64 Attitude 72 67 78 82 75 87 92 83 87 78 Use the given data to find the equation of the regression line.   y^ = - 47.3 + 2.02x y^ = 2.81 + 1.35x y^ = 11.7 + 1.02x y^ = 92.3 - 0.669x

a. what is the equation of the regression line? b. interpret r of the regression line  c. interpret r^2 of the regression line    L1 - 4,15,12,11,8,6,7,2,7,14,20,3,13 L2 - 120,200,140,110,120,80,190,100,120,190,190,110,120

^ The money raised and spent (both in millions of dollars) by all congressional campaigns for 8 recent 2-year periods are shown in the table. The equation of the regression line is y = 0.951x + 17.469. Find the coefficient of determination and interpret the result. Money raised, x 471.6 653.1 734.2 786.7 783.8 1044.8 954.2 1216.7 Money spent, y 436.2 689.2 729.3 766.4 726.7 1019.7 925.7 1163.9 Find the coefficient of determination and interpret the result. 2 = 1 (Round to three decimal places as needed.)

A multiple regression model has the form y^=b0+b1x1+b2x2 The coefficient b1 is interpreted as the:A. change in y per unit change in x1, holding x2 constantB. change in the average value of y per unit change in x1, holding x2 constantC. change in y per unit change in x1, when x1 and x2 values are correlatedD. change in y per unit change in x1 If multicollinearity exists among the independent variables included in a multiple regression model, the:A. multiple coefficient of determination will assume a value close to zeroB. standard errors of the regression coefficients for the correlated independent variables will increaseC. regression coefficients will be difficult to interpretD. regression coefficients will be difficult to interpret and the standard errors of the regression coefficients for the correlated independent variables will increase please explain which answer is correct and why

call: Researchers measured the percent 1m(formula = Symptoms - wear_mask, data - some_states) of people in 25 states who ʻknew someone with COVID symptoms' (ŷ) and regressed this on the percent of the population frequently wearing a mask in public (x). Residuals: Min -7.9167 -2.3306 -0.2469 2.5020 7. 3345 10 Median 30 Маx coefficients: (Intercept) 111.0981 wear_mask Estimate std. Error t value Pr (>|t|) 10. 5423 10. 538 2.82e-10 *** -8. 375 1. 94 e-08 *** -1.0419 0.1244 signif. codes: 0 ****' 0.001 ***' 0.01 **' 0.05 '.' 0.1 ' ' 1 Residual standard error: 3.859 on 23 degrees of freedom Multiple R-squared: 0.7531, F-statistic: 70.15 on 1 and 23 DF, p-value: 1.936e-08 Adjusted R-squared: 0.7423 If 75 percent of people in a state wear masks regularly, what % of people does this model predict will know someone with COVID symptons? 1) 32 2) 33 3) 34 4) 35

Benign prostatic hyperplasia is a noncancerous enlargement of the prostate gland that adversely affects the quality of life (QoL) of millions of men. A study of minimally invasive procedures for the treatment for this condition looked at pretreatment QoL (qol_base) and quality of life after 3 month on treatment (qol_3mo) The baseline data for 10 patients and their 3 month follow-up data is presented below: MAXFLO_B = maximum urine flow at baseline (urine flow measurement scale misplaced) MAXFLO3M = maximum urine flow after 3 months of treatment maxflo_b maxflo3m 7 8 18 8 13 9. 16 11 8 4 12 10 8 14 10 13

Does the Regression line give information about all the data points in the data set? Does the Regression line usually have all the points in the data set on it?

Find the best predicted value of y corresponding to the given value of x. ^ 21) Six pairs of data yield r = 0.789 and the regression equation y = 4x - 2. Also, y = 19.0. What is the best predicted value of y for x = 5? A) 18.0 B) 18.5 C) 19.0 D) 22.0 21)

true or false. Explain In a fixed effects regression, the residuals (ûit) will be uncorrelated with the estimated fixed effects.