Some data were collected on the weight of a male white laboratory rat for the first 25 weeks after its birth. A scatterplot of the weight (in grams) and time since birth (in weeks) shows a fairly strong, positive linear relationship. The linear regression equation weight = 100 + 40(time) models the data fairly well.
2. What’s the y intercept? Explain what it means in context.
The value of y-intercept is
We are given the linear regression equation of weight on time:
We know that for a linear regression equation of the form:
The value of y-intercept is a.
Therefore value of y-intercept for the given equation will be
The value of y-intercept that is means that if we were to keep the value of time 0, weight will be 100. That is initally we assume the weight to be
Teaching and research A college newspaper interviews a psychologist about student ratings of the teaching of faculty members. The psychologist says, “The evidence indicates that the correlation between the research productivity and teaching rating of faculty members is close to zero.” The paper reports this as “Professor McDaniel said that good researchers tend to be poor teachers, and vice versa.” Explain why the paper’s report is wrong. Write a statement in plain language (don’t use the word “correlation”) to explain the psychologist’s meaning.
Southern education For a long time, the South has lagged behind the rest of the United States in the performance of its schools. Efforts to improve education have reduced the gap. We wonder if the South stands out in our study of state average SAT Math scores.
The figure below enhances the scatterplot in Figure (page ) by plotting southern states in red.
(a) What does the graph suggest about the southern states?
(b) The point for West Virginia is labeled in the graph. Explain how this state is an outlier.
Joan is concerned about the amount of energy she uses to heat her home. The graph below plots the mean number of cubic feet of gas per day that Joan used each month against the average temperature that month (in degrees Fahrenheit) for one heating season.
(a) Does the plot show a positive or negative association between the variables? Why does this make sense?
(b) What is the form of the relationship? Is it very strong? Explain your answers.
(c) Explain what the point at the bottom right of the plot represents.
You have data for many years on the average price of a barrel of oil and the average retail price of a gallon of unleaded regular gasoline. If you want to see how well the price of oil predicts the price of gas, then you should make a scatterplot with ______ as the explanatory variable.
(a) the price of oil
(b) the price of gas
(c) the year
(d) either oil price or gas price
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