Which unit rate corresponds to the proportional relationship shown in the graph? Drag and drop the answer into the box to match
the graph with its unit rate. A graph with a line running through coordinates left parenthesis 0 comma 0 right parenthesis and coordinates left parenthesis 12 comma 16 right parenthesis . opitions- 0.33 cm/s 0.25 cm/s 0.75 cm/s 1.33 cm/s
The line is going from point (0;0) to point (12;16), the proportional relationship between these points refer to the slope of the line, which can be found with this expression:
Replacing all values we have:
Therefore the relation shown in the graph is represented by 1.33 cm/s, which refers to the constant speed developed by the object.
Here a pivotal quantity is where is the true slope of the regression equation (unknown), is its least square estimate and is its estimated standard error. And T has t-distribution with n-2=15-2=13 degrees of freedom (n is the sample size). We have that , and because we want the 95% confidence interval, we should use the 2.5th quantile of the t distribution with 13 df, this value is -2.16 and the 95% confidence intervale is given by , i.e., . Therefore, the 95% confidence interval explicitly is (-5.666, -0.926)