91影视

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.

How much gas? In Exercise $4$(page $158$), we examined the relationship between the average monthly temperature and the amount of natural gas consumed in Joan鈥檚 midwestern home. The 铿乬ure below shows the original scatterplot with the least-squares line added. The equation of the least-squares line is$\hat{y}=1425鈭�19.87x$

(a) Identify the slope of the line and explain what it means in this setting.

(b) Identify the y-intercept of the line. Explain why it鈥檚 risky to use this value as a prediction.

(c) Use the regression line to predict the amount of natural gas Joan will use in a month with an average temperature of $30$掳贵.

Acid rain Refer to Exercise $39$. Would it be appropriate to use the regression line to predict pH after$1000$ months? Justify your answer.

The residual plot does not show a random scatter. Describe the pattern you see.

How much gas? Refer to Exercise $40$. Would it be appropriate to use the regression line to predict Joan鈥檚 natural-gas consumption in a future month with an average temperature of $65$掳贵? Justify your answer

For this regression, $s=2.27$. Interpret this value in context.

Least-squares idea The table below gives a small set of data. Which of the following two lines 铿乼s the data better: $\hat{y}=1鈭�x\text{or}\hat{y}=3鈭�2x$? Make a graph of the data and use it to help justify your answer. (Note: Neither of these two lines is the least-squares regression line for these data.)

Least-squares ideaTrace the graph from Exercise $40$on your paper. Show why the line drawn on the plot is called the least-squares line.

Acid rain In the acid rain study of Exercise $39$, the actual pH measurement for Week $50$was$5.08$. Find and interpret the residual for this week.

How much gas? Refer to Exercise $40$. During March, the average temperature was $46.4$掳贵 and Joan used $490$ cubic feet of gas per day. Find and interpret the residual for this month.