Question

10.52  Predicting water quality for an area of 40 km². Refer to Exercise 10.48.( Please do only 10.52 )

1. (a) Find a 95% confidence interval for the mean response corresponding to an area of 40 km².

2. (b) Find a 95% prediction interval for a future response corresponding to an area of 40 km².

3. (c) Write a short paragraph interpreting the meaning of the intervals in terms of Ozark Highland streams.

4. (d) Do you think that these results can be applied to other streams in Arkansas or in other states? Explain why or why not.

5. Here Exercice 10.48 for the data

10.48  Predicting water quality. The index of biotic integrity (IBI) is a measure of the water quality in streams. IBI and land use measures for a collection of streams in the Ozark Highland ecoregion of Arkansas were collected as part of a study.²¹ Table 10.4 gives the data for IBI, the percent of the watershed that was forest, and the area of the watershed in square kilometers for streams in the original sample with watershed area less than or equal to 70 km².

1. (a) Use numerical and graphical methods to describe the variable IBI. Do the same for area. Summarize your results.

   TABLE 10.4 Watershed Area (km²), Percent Forest, and Index of Biotic Integrity

   Area	Forest	IBI	Area	Forest	IBI	Area	Forest	IBI	Area	Forest	IBI	Area	Forest	IBI
   21	0	47	29	0	61	31	0	39	32	0	59	34	0	72
   34	0	76	49	3	85	52	3	89	2	7	74	70	8	89
   6	9	33	28	10	46	21	10	32	59	11	80	69	14	80
   47	17	78	8	17	53	8	18	43	58	21	88	54	22	84
   10	25	62	57	31	55	18	32	29	19	33	29	39	33	54
   49	33	78	9	39	71	5	41	55	14	43	58	9	43	71
   23	47	33	31	49	59	18	49	81	16	52	71	21	52	75
   32	59	64	10	63	41	26	68	82	9	75	60	54	79	84
   12	79	83	21	80	82	27	86	82	23	89	86	26	90	79
   16	95	67	26	95	56	26	100	85	28	100	91

2. (b) Plot the data and describe the relationship between IBI and area. Are there any outliers or unusual patterns?

3. (c) Give the statistical model for simple linear regression for this problem.

4. (d) State the null and alternative hypotheses for examining the relationship between IBI and area.

5. (e) Run the simple linear regression and summarize the results.

6. (f) Obtain the residuals and plot them versus area. Is there anything unusual in the plot?

7. (g) Do the residuals appear to be approximately Normal? Give reasons for your answer.

8. (h) Do the assumptions for the analysis of these data using the model you gave in part (c) appear to be reasonable? Explain your answer.

Answer 1