An Economist Wanted to Analyse the Relationship Between the Speed

question 162

Essay

An economist wanted to analyse the relationship between the speed of a car (x) in kilometres per hour (kmph) and its fuel consumption (y) in kilometres per litre (kmpl). In an experiment, a car was operated at several different speeds and for each speed the fuel consumption was measured. The data obtained are shown below. $$\begin{array} { | l | l | l | l | l | l | l | l | } \hline \text { Speed (mph) } & 25 & 35 & 45 & 50 & 60 & 65 & 70 \\\hline \begin{array} { l } \text { Fuel consumtion } \\\text { (mpg) }\end{array} & 40 & 39 & 37 & 33 & 30 & 27 & 25 \\& & & & & & & \\\hline\end{array}$$ a. Find the least squares regression line.
b. Calculate the standard error of estimate, and describe what this statistic tells you about the regression line.
c. Do these data provide sufficient evidence at the 5% significance level to infer that a linear relationship exists between higher speeds and lower fuel consumption?
d. Predict with 99% confidence the fuel consumption of a car traveling at 55 kmph.

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Definitions:

Lev Vygotsky

A Russian psychologist known for his work on psychological development in children, emphasizing the role of social interaction and cultural tools in learning.

Number Conservation

A cognitive ability in children that demonstrates their understanding that quantity remains the same despite changes in shape or arrangement.

Preoperational Thought

A stage in Piaget's cognitive development theory characterized by symbolic thinking, egocentrism, and a lack of logical reasoning in children aged 2 to 7 years.

Centration

A characteristic of preoperational thought in which the child tends to focus on one salient feature of an experience or event at a time.