HypertensionThe 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 quantifythe 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 = 1,369Hint: 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-hoururinary Na on casual urinary measurementsand other risk factorsVariableInterceptCasual Na (mmol/L)Casual creatinine (mmol/L)Casual potassium (mmol/L)Body mass index (kg/m²)Age (years)Age² (years²)Beta25.42 16.650.42-2.71-0.12=se0.280.000.020.264.16 0.350.050.760.01(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 whetherother 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 factorsin 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 whetherother 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 inthe 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 factorsin 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-valueProvide 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.)

Question

HypertensionThe 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 quantifythe 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 = 1,369Hint: 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-hoururinary Na on casual urinary measurementsand other risk factorsVariableInterceptCasual Na (mmol/L)Casual creatinine (mmol/L)Casual potassium (mmol/L)Body mass index (kg/m²)Age (years)Age² (years²)Beta25.42 16.650.42-2.71-0.12=se0.280.000.020.264.16 0.350.050.760.01(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 whetherother 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 factorsin 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 whetherother 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 inthe 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 factorsin 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-valueProvide 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.)

Accepted Answer

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