# The linear correlation coeffic

The Minitab output shown below was obtained by using paired data consisting of weights​ (in lb) of 32 cars and their highway fuel consumption amounts​ (in mi/gal). Along with the paired sample​ data, Minitab was also given a car weight of 4500 lb to be used for predicting the highway fuel consumption amount. Use the information provided in the display to determine the value of the linear correlation coefficient.​ (Be careful to correctly identify the sign of the correlation​ coefficient.) Given that there are 32 pairs of​ data, is there sufficient evidence to support a claim of linear correlation between the weights of cars and their highway fuel consumption​ amounts?

 Predictor Coef  SE Coef  T P Constant The regression equation is Highway=50.5−0.00588 Weight 50.474 2.832 17.67 0.000 −0.0058772 0.0007753 −7.85 0.000 S=2.23963         R−Sq=65.9​%       R−​Sq(adj)=63.5​% Predicted Values for New Observations 1 24.027 0.523 (23.009, 25.045) (19.430, 28.624) Values of Predictors for New Observations 1 4500

The linear correlation coefficient is __.

(Round to three decimal places as​ needed.)

Is there sufficient evidence to support a claim of linear​correlation?

-no
-yes

# The linear correlation coeffic

Listed below are numbers of Internet users per 100 people and numbers of scientific award winners per 10 million people for different countries. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the​ P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of α=0.01.

Internet Users (Per 100) Award Winners (Per 10 Million)
80.6                                5.4
78.1                                8.9
56.5                                3.3
68.3                                1.6
78.9                                10.9
38.8                                 0.1

C

The linear correlation coefficient is r=__

(round to three decimal places as needed)

=0/=0

The test statistic is t= __

(Round to two decimal places as​ needed.)

The P-value is __

(round to three decimal places as needed)

Because the​ P-value of the linear correlation coefficient is (less than or equal to/greater than) the significance​ level, there (is/is not) sufficient evidence to support the claim that there is a linear correlation between internet users and scientific award winners.

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