Final answer:
The question involves using linear regression in R to analyze a data set of weights measured two at a time.
Step-by-step explanation:
The question is about applying linear regression analysis to a data set of paired weights measured by a spring balance. It involves using the lm() function in R to fit a model to the data. The observed values for six measurements are given as (Y1, Y2, Y3, Y4, Y5, Y6) = (5, 8, 6, 7, 10, 9). The task includes fitting the data using linear regression and checking the results for the following:
- Scatter plot creation for the data.
- Least-squares line calculation, writing the equation in the form ŷ = a + bx.
- Drawing the least-squares line on the scatter plot.
- Finding the correlation coefficient and its significance.
- Use of the lm() function to fit the data and comparing its output to the derived least-squares line.
To begin, we decide the dependent and independent variables and plot a scatter plot. Through inspection, we can hypothesize whether there is a relationship between the variables before computing the least-squares regression line and the correlation coefficient.
For example, if the observations represent data such as height and weight, we might conjecture that a positive relationship exists, as taller individuals generally weigh more. The strength and significance of this hypothetical relationship would then be quantified by the correlation coefficient calculated from our regression analysis.