Question

Chirp Rate (chirps/sec) Temperature (F) 2.4 61.9 3.8 83.6 3.7 71.8 2.0 47 3.4 65.1 3.9 75.8

Answer 1

Answer:

Here to answer this question we use MINITAB software,

1.

First we enter the values of chirp rate and Temperature. Then we use the path:

Stat> Basic Statistics> Correlation > then select these two variables > OK.

Output is:

Pearson correlation of Chip Rate and Temperature = 0.908

Hence coefficient of correlation is 0.908

2.

Now use path:

Stat> Regression > then select both response and predictor variable > OK.

Output is:

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant 21.6 10.8 1.99 0.117
Chip Rate 14.35 3.30 4.35 0.012 1.00

Regression Equation

Temperature = 21.6 + 14.354 Chip Rate

As we know x is chirp rate and y is temparature, so the regression equation will be :

y = 21.6 + 14.354x. So option 4 is correct .

3.

Now here chirp rate is 3.2 and temperature is calculated as:

y = 21.6 + 14.354*3.2 = 45.9328

Hence temperature is 45.9328

Excel output for reference:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.90842
R Square	0.825227
Adjusted R Square	0.781533
Standard Error	5.92684
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	663.4436	663.4436	18.88677	0.012196
Residual	4	140.5097	35.12743
Total	5	803.9533
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	21.60041	10.8427	1.992162	0.117161	-8.50375	51.70458
Chip Rate	14.35404	3.302899	4.345891	0.012196	5.18372	23.52435

Here multiple R is correlation coefficient. and regression equation is obtained from coefficients.