Final answer:
To assess if there's a linear relationship between the Gesell score and the age at first word, one would create a scatterplot with the Gesell score as (y) and age as (x). The presence of a linear trend could be indicated by a clustering of points near a line, while the strength of the relationship would be further analyzed using the least-squares regression line and correlation coefficient.
Step-by-step explanation:
To determine whether there is a linear relationship between the Gesell adaptive score test (Gesell score) and the age at which children speak their first word, you would start by plotting a scatterplot with the Gesell score as the response variable (y) and the age at first word as the explanatory variable (x). In the scatterplot, each point represents one child's data with their corresponding age at first word on the x-axis and Gesell score on the y-axis.
After plotting the data, you would examine the scatterplot to see if the points suggest a linear trend. If the points cluster around a line that slopes upwards or downwards, this could indicate a positive or negative linear relationship respectively. Conversely, if the points are widely scattered without any discernible pattern, it might suggest that there is no significant relationship between the variables.
If there seems to be a potential linear relationship, you might proceed to calculate the least-squares regression line to find the best-fitting line through the data and the correlation coefficient to measure the strength and direction of the relationship between the variables. Significant correlation coefficients (typically those near -1 or 1) would support the presence of a linear relationship, while coefficients near zero would suggest little to no linear relationship.