Considering a Situation where You Want to Determine if There is a Linear Model Connecting Protein and Carbohydrates in the Entire Population of Foods from Starbucks
When considering a situation where you are interested in determining whether or not there is a linear model connecting protein and carbohydrates in the entire population of foods from Starbucks, we will walk through the pieces of the linear model output and then in the following chapters, we will explore all the pieces of inference in further detail. The variables in the Starbucks dataset include calories, fat, carbohydrates, fiber, and protein.
If interest is in determining a linear relationship between two of the variables, we can approach the linear model investigation in two ways: with a one-sided or two-sided hypothesis. A two-sided research question investigates whether the two variables are linearly associated in the population, while a one-sided research question investigates whether the two variables have a positive linear association. To avoid excess false positives, the research question is always decided on before looking at the data.
Note that there are two different but similar ways to output the linear model information. Recall that the estimates have been calculated using least squares optimization. The value for the slope is 0.38, and it is exactly the same regardless of the format of the output. As with the slope, the intercept (37.1) is given in the long or tidy format. The variability of both the intercept and the slope are given in the column called standard error.
The standard error represents how much the line varies in units associated with either the intercept row 1 or the slope row 2. In both outputs, there is a column labeled "statistic" which combines the least squares estimate with the standard error. The statistic is a standardized estimate that measures the number of standard errors that the estimate is above 0. As with the estimate and standard error, the intercept statistic is given in the first row, and the slope statistic is given in the second row.
The information for testing whether either the intercept or the slope is zero is given by the p-value in the last column of the output. The default test is two-sided, and it is important to keep in mind that you don't know what your research question is for the model at hand. It is easy to reject the value of zero as a plausible value for the intercept, as there's virtually no possible way for data like these to have come from a population with an intercept of zero.
On the other hand, the slope has a significant p-value of 0.03. However, the p-value tells us that if there is no relationship between protein and carbs in the population, we would see data like these about three percent of the time. If the original research question had been one-sided, that is, our protein and carbs positively associated, the p-value should be divided by two to arrive at a one-sided p-value of about 0.01. Five, the data are substantially more significant when testing a one-sided hypothesis although the one-sided test should only be used if the original research question is also one-sided.
Thanks for following along with this video now.
"WEBVTTKind: captionsLanguage: enconsider a situation where you are interested in determining whether or not there is a linear model connecting protein and carbohydrates in the entire population of foods from Starbucks we will walk through the pieces of the linear model output and then in the following chapters we will explore all the pieces of inference in further detail the variables in the Starbucks dataset include calories fat carbohydrates fiber and protein if interest is in determining a linear relationship between two of the variables we can approach the linear model investigation in two ways with a one-sided or two-sided hypothesis a two-sided research question investigates whether the two variables are linearly associated in the population a one-sided research question in this scenario investigates whether the two variables have a positive linear Association in order to avoid excess false positives the research question is always decided on before looking at the data note that two different but similar ways to output the linear model information recall that the estimates have been calculated using least squares optimization the value for the slope 0.38 one is exactly the same regardless of the format of the output as with the slope the intercept 37 point 1 is given in the long or tidy format the variability of both the intercept and the slope are given in the column called standard error the standard error represents how much the line varies in units associated with either the intercept row 1 or the slope row 2 in both outputs there is a column labeled statistic which combines the least squares estimate with the standard error the statistic is a standardized estimate it measures the number of standard errors that the estimate is above 0 as with the estimate and standard error the intercept statistic is given the first row and the slope statistic is given in the second row last the information for testing whether either the intercept or the slope is zero is given by the p-value in the last column of the output the default test is two-sided and it is important to keep in mind that are doesn't know what your research question is for the model at hand it is easy to reject the value of zero as a plausible value for the intercept that is there's virtually no possible way for data like these to have come from a population with an intercept of zero the slope on the other hand has a significant p-value of 0.03 but the p-value tells us that if there is no relationship between protein and carbs in the population we would see data like these about three percent of the time if the original research question had been one-sided that is our protein and carbs positively associated the p-value should be divided by two to arrive at a one-sided p-value of about 0.01 five the data are substantially more significant when testing a one-sided hypothesis although the one-sided test should only be used if the original research question is also one-sided thanks for following along with this video nowconsider a situation where you are interested in determining whether or not there is a linear model connecting protein and carbohydrates in the entire population of foods from Starbucks we will walk through the pieces of the linear model output and then in the following chapters we will explore all the pieces of inference in further detail the variables in the Starbucks dataset include calories fat carbohydrates fiber and protein if interest is in determining a linear relationship between two of the variables we can approach the linear model investigation in two ways with a one-sided or two-sided hypothesis a two-sided research question investigates whether the two variables are linearly associated in the population a one-sided research question in this scenario investigates whether the two variables have a positive linear Association in order to avoid excess false positives the research question is always decided on before looking at the data note that two different but similar ways to output the linear model information recall that the estimates have been calculated using least squares optimization the value for the slope 0.38 one is exactly the same regardless of the format of the output as with the slope the intercept 37 point 1 is given in the long or tidy format the variability of both the intercept and the slope are given in the column called standard error the standard error represents how much the line varies in units associated with either the intercept row 1 or the slope row 2 in both outputs there is a column labeled statistic which combines the least squares estimate with the standard error the statistic is a standardized estimate it measures the number of standard errors that the estimate is above 0 as with the estimate and standard error the intercept statistic is given the first row and the slope statistic is given in the second row last the information for testing whether either the intercept or the slope is zero is given by the p-value in the last column of the output the default test is two-sided and it is important to keep in mind that are doesn't know what your research question is for the model at hand it is easy to reject the value of zero as a plausible value for the intercept that is there's virtually no possible way for data like these to have come from a population with an intercept of zero the slope on the other hand has a significant p-value of 0.03 but the p-value tells us that if there is no relationship between protein and carbs in the population we would see data like these about three percent of the time if the original research question had been one-sided that is our protein and carbs positively associated the p-value should be divided by two to arrive at a one-sided p-value of about 0.01 five the data are substantially more significant when testing a one-sided hypothesis although the one-sided test should only be used if the original research question is also one-sided thanks for following along with this video now\n"
