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The investigators for a study collected standardized data on timed 24-hour urinary excretion for 10,079 men and women from 52 population samples in 32 countries. One of the goals of the study was to quantify the relationship between 24-hour urinary Na (y) and estimated 24-hour urinary Na (x) obtained from casual urine specimens at one point in time. The investigators presented a simple linear regression of y on x, separately for men and women. The regression equation for men was: Y = 1.09x - 7.11, with R2 = 0.26, n = 1,369 Hint: Assume that a t distribution with > 200 df is the same as a N(0, 1) distribution. You can use the Distribution Calculators page in SALT to find critical values and/or p-values to answer parts of this question. (a) What does the R2 of 0.26 mean in words? OR² = 0.26 means that about 74% of the time the estimated 24-hour urinary Na matches the 24-hour urinary Na obtain from casual urine specimens at one point in time. O R² = 0.26 means that about 26% of the variation in 24-hour urinary Na can be explained by estimated 24-hour urinary Na obtain from casual urine specimens at one point in time. O R² = 0.26 means that about 26% of the time the estimated 24-hour urinary Na matches the 24-hour urinary Na obtain from casual urine specimens at one point in time. OR² = 0.26 means that about 74% of the variation in 24-hour urinary Na can be explained by estimated 24-hour urinary Na obtain from casual urine specimens at one point in time. (b) What is a two-sided p-value for the regression? (Round your answer to four decimal places.) (c) What is the estimated standard error of the slope estimate? (Hint: Use the t test for simple linear regression. Round your answer to four decimal places.)

The investigators for a study collected standardized data on timed 24-hour urinary excretion for 10,079 men and women from 52 population samples in 32 countries. One of the goals of the study was to quantify the relationship between 24-hour urinary Na (y) and estimated 24-hour urinary Na (x) obtained from casual urine specimens at one point in time. The investigators presented a simple linear regression of y on x, separately for men and women. The regression equation for men was: Y = 1.09x - 7.11, with R2 = 0.26, n = 1,369 Hint: Assume that a t distribution with > 200 df is the same as a N(0, 1) distribution. You can use the Distribution Calculators page in SALT to find critical values and/or p-values to answer parts of this question. (a) What does the R2 of 0.26 mean in words? OR² = 0.26 means that about 74% of the time the estimated 24-hour urinary Na matches the 24-hour urinary Na obtain from casual urine specimens at one point in time. O R² = 0.26 means that about 26% of the variation in 24-hour urinary Na can be explained by estimated 24-hour urinary Na obtain from casual urine specimens at one point in time. O R² = 0.26 means that about 26% of the time the estimated 24-hour urinary Na matches the 24-hour urinary Na obtain from casual urine specimens at one point in time. OR² = 0.26 means that about 74% of the variation in 24-hour urinary Na can be explained by estimated 24-hour urinary Na obtain from casual urine specimens at one point in time. (b) What is a two-sided p-value for the regression? (Round your answer to four decimal places.) (c) What is the estimated standard error of the slope estimate? (Hint: Use the t test for simple linear regression. Round your answer to four decimal places.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Hypertension The investigators for a study collected standardized data on timed 24-hour urinary excretion for 10,079 men and women from 52 population samples in 32 countries. One of the goals of the study was to quantify the relationship between 24-hour urinary Na (y) and estimated 24-hour urinary Na (x) obtained from casual urine specimens at one point in time. The investigators presented a simple linear regression of y on x, separately for men and women. The regression equation for men was: Y = 1.09x - 7.11, with R² = 0.26, n = 1,369 Hint: Assume that a t distribution with > 200 df is the same as a N(0, 1) distribution. You can use the Distribution Calculators page in SALT to find critical values and/or p-values to answer parts of this question. (a) What does the R² of 0.26 mean in words? R²: = 0.26 means that about 74% of the time the estimated 24-hour urinary Na matches the 24-hour urinary Na obtain from casual urine specimens at one point in time. R² = 0.26 means that about 26% of the variation in 24-hour urinary Na can be explained by estimated 24-hour urinary Na obtain from casual urine specimens at one point in time. R² = 0.26 means that about 26% of the time the estimated 24-hour urinary Na matches the 24-hour urinary Na obtain from casual urine specimens at one point in time. OR² = 0.26 means that about 74% of the variation in 24-hour urinary Na can be explained by estimated 24-hour urinary Na obtain from casual urine specimens at one point in time. (b) What is a two-sided p-value for the regression? (Round your answer to four decimal places.) (c) What is the estimated standard error of the slope estimate? (Hint: Use the t test for simple linear regression. Round your answer to four decimal places.) (d) Provide a 95% CI for the true slope (B). (Enter your answer using interval notation. Round your numerical values to two decimal places.)
Transcribed Image Text:Hypertension The investigators for a study collected standardized data on timed 24-hour urinary excretion for 10,079 men and women from 52 population samples in 32 countries. One of the goals of the study was to quantify the relationship between 24-hour urinary Na (y) and estimated 24-hour urinary Na (x) obtained from casual urine specimens at one point in time. The investigators presented a simple linear regression of y on x, separately for men and women. The regression equation for men was: Y = 1.09x - 7.11, with R² = 0.26, n = 1,369 Hint: Assume that a t distribution with > 200 df is the same as a N(0, 1) distribution. You can use the Distribution Calculators page in SALT to find critical values and/or p-values to answer parts of this question. (a) What does the R² of 0.26 mean in words? R²: = 0.26 means that about 74% of the time the estimated 24-hour urinary Na matches the 24-hour urinary Na obtain from casual urine specimens at one point in time. R² = 0.26 means that about 26% of the variation in 24-hour urinary Na can be explained by estimated 24-hour urinary Na obtain from casual urine specimens at one point in time. R² = 0.26 means that about 26% of the time the estimated 24-hour urinary Na matches the 24-hour urinary Na obtain from casual urine specimens at one point in time. OR² = 0.26 means that about 74% of the variation in 24-hour urinary Na can be explained by estimated 24-hour urinary Na obtain from casual urine specimens at one point in time. (b) What is a two-sided p-value for the regression? (Round your answer to four decimal places.) (c) What is the estimated standard error of the slope estimate? (Hint: Use the t test for simple linear regression. Round your answer to four decimal places.) (d) Provide a 95% CI for the true slope (B). (Enter your answer using interval notation. Round your numerical values to two decimal places.)
The actual regression equation used to derive the estimated 24-hour urinary Na for men in North America also included several additional variables and was as follows. Multiple linear regression of 24-hour urinary Na on casual urinary measurements and other risk factors Variable Intercept Casual Na (mmol/L) Casual creatinine (mmol/L) Casual potassium (mmol/L) Body mass index (kg/m²) Age (years) Age² (years²) Beta 25.42 16.65 0.42 -2.71 -0.12 = se 0.28 0.00 0.02 0.26 4.16 0.35 0.05 0.76 0.01 (e) What does the regression coefficient for casual potassium (-0.12) mean in words? The regression coefficient of -0.12 means that for every 1 mmol/L increase in casual urinary potassium, there is an expected decrease of 0.12 mmol/L in 24-hour urinary Na regardless of whether other factors are changing along with casual urinary potassium. The regression coefficient of -0.12 means that for every 1 mmol/L increase in casual urinary potassium, there is an expected increase of 0.12 mmol/L in 24-hour urinary Na, holding all other factors in the multiple regression equation constant. The regression coefficient of -0.12 means that for every 1 mmol/L increase in casual urinary potassium, there is an expected increase of 0.12 mmol/L in 24-hour urinary Na regardless of whether other factors are changing along with casual urinary potassium. The regression coefficient of -0.12 means that for every 1 kg/m² increase in casual urinary potassium, there is an expected decrease of 0.12 kg/m² in 24-hour urinary Na, holding all other factors in the multiple regression equation constant. The regression coefficient of -0.12 means that for every 1 mmol/L increase in casual urinary potassium, there is an expected decrease of 0.12 mmol/L in 24-hour urinary Na, holding all other factors in the multiple regression equation constant. (f) Provide a two-sided p-value associated with the regression coefficient for casual potassium (-0.12). (Round your answer to four decimal places.) p-value Provide a 95% Cl associated with the regression coefficient for casual potassium (-0.12). (Enter your answer using interval notation. Round your numerical values to two decimal places.)
Transcribed Image Text:The actual regression equation used to derive the estimated 24-hour urinary Na for men in North America also included several additional variables and was as follows. Multiple linear regression of 24-hour urinary Na on casual urinary measurements and other risk factors Variable Intercept Casual Na (mmol/L) Casual creatinine (mmol/L) Casual potassium (mmol/L) Body mass index (kg/m²) Age (years) Age² (years²) Beta 25.42 16.65 0.42 -2.71 -0.12 = se 0.28 0.00 0.02 0.26 4.16 0.35 0.05 0.76 0.01 (e) What does the regression coefficient for casual potassium (-0.12) mean in words? The regression coefficient of -0.12 means that for every 1 mmol/L increase in casual urinary potassium, there is an expected decrease of 0.12 mmol/L in 24-hour urinary Na regardless of whether other factors are changing along with casual urinary potassium. The regression coefficient of -0.12 means that for every 1 mmol/L increase in casual urinary potassium, there is an expected increase of 0.12 mmol/L in 24-hour urinary Na, holding all other factors in the multiple regression equation constant. The regression coefficient of -0.12 means that for every 1 mmol/L increase in casual urinary potassium, there is an expected increase of 0.12 mmol/L in 24-hour urinary Na regardless of whether other factors are changing along with casual urinary potassium. The regression coefficient of -0.12 means that for every 1 kg/m² increase in casual urinary potassium, there is an expected decrease of 0.12 kg/m² in 24-hour urinary Na, holding all other factors in the multiple regression equation constant. The regression coefficient of -0.12 means that for every 1 mmol/L increase in casual urinary potassium, there is an expected decrease of 0.12 mmol/L in 24-hour urinary Na, holding all other factors in the multiple regression equation constant. (f) Provide a two-sided p-value associated with the regression coefficient for casual potassium (-0.12). (Round your answer to four decimal places.) p-value Provide a 95% Cl associated with the regression coefficient for casual potassium (-0.12). (Enter your answer using interval notation. Round your numerical values to two decimal places.)
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