Question

For the following correlated data:

Set#1(std conc ppm) is 1.5, 6.5, 11.2, 21.5, and 35.1. Set#2(system response) is 0.7, 4.8, 13.2, 42.8, and 59.3.
a.) Calculate the Least Squares slope.
b.) Calculate the least squares intercept.
c.) If set#1 corresponds to concentration in ppm and set #2 is sample response, what would be the response of an 11 ppm sample?
d.) Calculate the correlation coefficient for the above data sets.

Answer 1

Linear regression analysis to calculate the least squares slope and intercept for given data sets, estimating responses for specific concentrations, and determining the correlation coefficient to evaluate the relationship's strength.

Step-by-step explanation:

To address the student's question regarding the correlation of data sets, we'll perform a linear regression analysis using the least squares method.

1. First, set#1, which represents the standard concentration in parts per million (ppm), is the independent variable, and set#2, indicative of the system response, the dependent variable.
2. Then, we calculate the least squares slope (b) and intercept (a) using the linear regression formula ŷ = a + bx.
3. Next, we use these values to estimate the system response for an 11 ppm sample of set#1.
4. Finally, we calculate the correlation coefficient to determine the strength and direction of the linear relationship between the two sets.

The slope and intercept from the least squares method allow us to predict system responses for given concentrations. The correlation coefficient helps us to understand whether the predicted values are likely to be accurate representations of the real-world relationships between concentration and response.