Use the technology of your choice to do the following tasks. The National Oceanic and Atmospheric Administration publishes temperature and precipitati

Kye 2020-12-30 Answered
Use the technology of your choice to do the following tasks. The National Oceanic and Atmospheric Administration publishes temperature and precipitation information for cities around the world in Climates of the World. Data on average high temperature (in degrees Fahrenheit) in July and average precipitation (in inches) in July for 48 cities are on the WeissStats CD. For part (d), predict the average July precipitation of a city with an average July temperature of 83F a) Construct and interpret a scatterplot for the data. b) Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c)-(f). c) Determine and interpret the regression equation. d) Make the indicated predictions. e) Compute and interpret the correlation coefficient. f) Identify potential outliers and influential observations.
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Aamina Herring
Answered 2020-12-31 Author has 85 answers

Given: n=Sa size=48 a) IMR is on the horizontal axis and LE is on the vertical axis. image b) When there is no strong curvature presents in the scatterplot, then it is safe to assume that there is a linear relationship between the variables and thus it is then reasonable to find a regression line. We note that the scatterplot of part (a) does not contain strong curvature and thus is reasonable to find the regression line. c) We determine all necessary sums:  xi=3749
 yi=123.3
 xi yi=9681.9
 xi2=300561
 yi2=584.99 Next, we can determine Sxx and Sxy
Sxx=  xi2=300561  3749248=39602.1698
Sxy=  xi yi  ( xi) ( yi)n=9681.9  3749  123.348= 14009.0727 The estimate b of the slope β is the ratio of Sxy and Sxx:
b= SxySxx= 14009.072739602.1698=0.0067 The mean is the sum of all values divided by the number of values: x=  xin= 374948=78.1042
y=  {yi}{n}= 123.348=2.5688 The estimate a of the intercept α is the average of y decresed by the product of the estimate of the slope and the average of x
a= y  bx=2.5688  0.0067  78.1042=2.0481 General least-squares equation: y^= α + β x. Replace α by a=2.0481 and β by b=0.0067 in the general least-squres equation
y^=a + bx=2.0481 + 0.0067x
image d) Let us evalute the regression line in part (c) at x=83:

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