I performed a linear regression and I got a p-value &lt; 0.05 but my R^2 is low (&lt; 0.04). How can I interpret the results? The model is significant but there's not a good fit, what can I do to solve this? (without affecting too much of my p-value) Thank you
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As far as I understand, a high F-stat leads to a high $R^2$, though the converse is not true. What does it mean if I have a high F-stat and a low $R^2$?
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Suppose, I have performed multiple regression analysis on the following data set where X1 and X2 are independent variables and Y is the dependent variable.    And achieved the following multiple regression analysis table from where it is clear that X2 is not correlated with Y as the p-value is greater than 0.05 which is 0.108 for X2 variable     So, if p value is greater than 0.05 for a variable, then why it is considered in regression equation  Y = 2.709 + 0.763(X1) + 0.463(X2) which has been shown in any online multiple regression equation calculator.  My question is Why it is not like the following Y = 2.709 + 0.763(X1) omitting the [0.463(X2)] part from the equation, as X2 is not correlated with Y  Please help to clarify the conceptual idea....
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My multiple regression analysis model has a statistically significant F value however all beta values are statistically non-significant.   All the regression assumptions are met. No multicollinearity was found. Correlations among all predictors are all less than 0.60.   What else might be the cause of the insignificant predictors?
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I am running into a problem where an independent variable, which should have no predictive power on the dependent variable based on domain knowledge, comes out with very small p-value because the sample size is very large(~100,000). If I only use &lt; 5000 data points, then the p-value becomes large enough to support the prior that the variable is insignificant. However, I don't think tweaking the sample size to get to the desired conclusion is a good practice. Is there any procedure to adjust for small p-value simply due to huge sample size?
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I am trying to calibrate two variables $(X,Y)$ of different measuring techniques from two instruments, the result of the linear regression analysis appears as shown in the image. The result shows the regression constant is not statistically significant but the model is significant. I have tried to remove the regression constant (it is a very small value close to zero) and $R$ of the new model is raised to 90%. Is it correct to remove the regression constant?
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My dependent variable shown below doesn't fit any stock distribution that I know of.  Linear regression produces somewhat non-normal, right-skewed residuals that relate to predicted Y in an odd way (2nd plot).  Any suggestions for transformations or other ways to obtain most valid results and best predictive accuracy?  If possible I'd like to avoid clumsy categorizing into, say, 5 values (e.g., 0, lo%, med%, hi%, 1).
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I cannot understand the usage of polynomial contrasts in regression fitting. In particular, I am referring to an encoding used by R in order to express an interval variable (ordinal variable with equally spaced levels), described at .  In the example of , if I understood correctly, R fits a model for an interval variable, returning some coefficients which weights its linear, quadratic, or cubic trend. Hence, the fitted model should be:  $${\rm write} = 52.7870 + 14.2587X - 0.9680X^2 - 0.1554X^3,$$  where $X$ should take values $1$, $2$, $3$, or $4$ according to the different level of the interval variable.  Is this correct? And, if so, what was the purpose of polynomial contrasts?
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I am running linear regression models and wondering what the conditions are for removing the intercept term.   In comparing results from two different regressions where one has the intercept and the other does not, I notice that the $R^2$ of the function without the intercept is much higher. Are there certain conditions or assumptions I should be following to make sure the removal of the intercept term is valid?
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I have a linear regression with two explanatory variables. One of them is a two level categorical variable. When I perform the fit, R tells me that the intercept is highly non significant. When I force the intercept to be zero in the regression, it tells me that the coefficient for the 0-level of the categorical variable is highly non significant. What should I do?
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I am trying to produce a model for which I have a response variable which is a proportion between 0 and 1, this includes quite a few 0s and 1s but also many values in between. I am thinking about attempting a beta regression. The package I have found for R (betareg) only allows values  in between 0 and 1 but not including 0 or 1 them selves. I have read elsewhere that theoretically the beta distribution should be able to handle values of 0 or 1 but I do not know how to handle this in R.I have seen some people add 0.001 to the zeros and take 0.001 from the ones, but I am not sure this is a good idea?  Alternatively I could logit transform the response variable and use linear regression. In this case I have the same problem with the 0 and 1's which cannot be log transformed.
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I am testing Mann-Whitney rank test with two vectors a and b. Vectors are almost similar so I expect a p-value near 0, but the returned p-value is near 1. What is the reason? I read  and also run the code with different parameters, but don't get anything near to what I expect.  from scipy.stats import mannwhitneyu import operator import numpy as np  a = [1000,100,10,1,10,100,1000,10000,1000,100,10,1] b = [999,100,10,1,10,100,1000,10000,1000,100,10,1]  print(mannwhitneyu(a, b))   The output of the code:  MannwhitneyuResult(statistic=73.5, pvalue=0.95291544831453867)   Edit:  Let's formalize the problem to eliminate any misunderstanding (please edit the question if something is wrong):  What I try to prove is that rank distribution of data are approximately equal,   Null hypothesis ($H_0$)= "ranked distribution of a and b are approximately equal"  Alternative hypothesis ($H_a$)= "ranked distribution of a and b are not equal"  significance level (alpha) = 0.05  p-value= 0.95  (p-value > alpha) so there is no sufficient evidence that $H_a$ is correct, but we cannot also conclude that ($H_0$) is true.   Instead if (p-value &lt; alpha) was true, then we would have enough evidence against H0 and Ha can be accepted.  So what happened here is that I could not disprove the null hypothesis. However, it doesn't mean that null hypothesis is false. It is like an investigation to accuse MR X of being guilty:   $H_0$=" MR X guilty" $H_a$=" MR X not guilty"  We guess he is not guilty, but we don't have enough proof against him: (p-value > alpha), but that doesn't mean that ($H_0$) would not be true. If we could obtain enough evidence and state (p-value &lt; alpha), then we disprove $H_0$ and we can conclude that Ha is true and he is not guilty.
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I'm using R to run some logistic regression. My variables were continuous, but I used cut to bucket the data. Some particular buckets for these variables always result in dependent variable being equal to 1. As expcted, the coefficient estimate for this bucket is very high, but the p-value is also high. There are about ~90 observations in either these buckets, and around 800 total observations, so I don't think it's a problem of sample size. Also, this variable should not be related to other variables, which would naturally reduce their p-values.  Are there any other plausible explanations for the high p-value?  Example:  myData &lt;- read.csv("application.csv", header = TRUE) myData$FICO &lt;- cut(myData$FICO, c(0, 660, 680, 700, 720, 740, 780, Inf), right = FALSE) myData$CLTV &lt;- cut(myData$CLTV, c(0, 70, 80, 90, 95, 100, 125, Inf), right = FALSE) fit &lt;- glm(Denied ~ CLTV + FICO, data = myData, family=binomial())   Results are something like this:  Deviance Residuals:       Min        1Q    Median        3Q       Max   -1.53831  -0.77944  -0.62487   0.00027   2.09771    Coefficients:                 Estimate Std. Error z value Pr(&gt;|z|)     (Intercept)     -1.33630    0.23250  -5.747 9.06e-09 *** CLTV(70,80]     -0.54961    0.34864  -1.576 0.114930     CLTV(80,90]     -0.51413    0.31230  -1.646 0.099715 .   CLTV(90,95]     -0.74648    0.37221  -2.006 0.044904 *   CLTV(95,100]     0.38370    0.37709   1.018 0.308906     CLTV(100,125]   -0.01554    0.25187  -0.062 0.950792     CLTV(125,Inf]   18.49557  443.55550   0.042 0.966739     FICO[0,660)     19.64884 3956.18034   0.005 0.996037     FICO[660,680)    1.77008    0.47653   3.715 0.000204 *** FICO[680,700)    0.98575    0.30859   3.194 0.001402 **  FICO[700,720)    1.31767    0.27166   4.850 1.23e-06 *** FICO[720,740)    0.62720    0.29819   2.103 0.035434 *   FICO[740,780)    0.31605    0.23369   1.352 0.176236     --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  (Dispersion parameter for binomial family taken to be 1)      Null deviance: 1037.43  on 810  degrees of freedom Residual deviance:  803.88  on 798  degrees of freedom AIC: 829.88  Number of Fisher Scoring iterations: 16   FICO in the range [0, 660) and CLTV in the range (125, Inf] indeed always results in Denial = 1, so their coefficients are very large, but why are they also "insignificant"?
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I did a toy experiment with linear regression, but getting different results for $R^2$, could any one help me?  library(ggplot2) fit=lm(price~carat+depth+table+x+y+z-1,data=diamonds) summary(fit) sse=crossprod(diamonds$price-fit$fitted.values) sst=crossprod(diamonds$price-mean(diamonds$price)) 1-sse/sst
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I'm performing a GLM, the response variable is number of individuals, and response variables are    habitat (4 levels) and  season (4 levels).    I need some help since I know the summary() shows p-values but not for the first (alphabetical) level of factor. I mean, I don't know how to interpret that the Intercept has a significant p-value. I can't reach a biological explanation for this model. Hope you can help me ...  Call: glm(formula = individuals ~ habitat + season, family = poisson(link = "log"),  data = data)  Deviance Residuals:   Min        1Q    Median        3Q       Max   -2.85859  -0.51541  -0.08508   0.36497   2.29058    Coefficients:                  Estimate Std. Error z value Pr(&gt;|z|)     (Intercept)            1.6774     0.1624  10.331  &lt; 2e-16 *** habitatDeciduous       0.1340     0.1696   0.790  0.42950     habitatSemiDeciduous   0.2102     0.1675   1.255  0.20933     habitatWetland        -0.1861     0.2039  -0.912  0.36151     seasondry2018         -0.1138     0.1510  -0.753  0.45123     seasonwet2016         -0.2699     0.1576  -1.713  0.08677 .   seasonwet2017         -0.4383     0.1656  -2.647  0.00813 **   Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  (Dispersion parameter for poisson family taken to be 1)  Null deviance: 78.487  on 63  degrees of freedom Residual deviance: 64.556  on 57  degrees of freedom AIC: 287.77
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I start with my OLS regression: $$ y = \beta _0 + \beta_1x_1+\beta_2 D + \varepsilon  $$ where D is a dummy variable, the estimates become different from zero with a low p-value. I then preform a Ramsey RESET test and find that i have some misspesification of the equation, i thus include squared x: $$ y = \beta _0 + \beta_1x_1+\beta_2x_1^2+\beta_3 D + \varepsilon  $$   What does the squared term explain? (Non-linear increase in Y?)  By doing this my D estimate does not vary from zero any more, with a high p-value. How do i interpret the squared term in my equation (in general)?   Edit: Improving question.
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I have a question on how a statistician would normally interpret an anova output. Say I have anova output from R.  &gt; summary(fitted_data)  Call: lm(formula = V1 ~ V2)  Residuals:      Min       1Q   Median       3Q      Max  -2.74004 -0.33827  0.04062  0.44064  1.22737   Coefficients:             Estimate Std. Error t value Pr(&gt;|t|)     (Intercept)  2.11405    0.32089   6.588  1.3e-09 *** V2           0.03883    0.01277   3.040  0.00292 **  --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1   Residual standard error: 0.6231 on 118 degrees of freedom Multiple R-squared: 0.07262,    Adjusted R-squared: 0.06476  F-statistic:  9.24 on 1 and 118 DF,  p-value: 0.002917   &gt; anova(fit) Analysis of Variance Table  Response: V1            Df Sum Sq Mean Sq F value   Pr(&gt;F)    V2          1  3.588  3.5878  9.2402 0.002917 ** Residuals 118 45.818  0.3883                     --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1    From the above, I guess the most important value is Pr(>F), right? So this Pr, is less than 0.05 (95% level). How should my "explain" this? Do I explain it in "association", ie, V2 and V1 are associated (or not) ? or in terms of "significance"? I always felt that I couldn't understand when people say "This value is significant....". So what is "significant"? Is there a more intuitive form of explanation? like "I am 95% confident that ...." .   Also, is the Pr value the only important piece of information? or can i also look at residuals and the rest of the output to "explain" the result? thanks
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As I was working my way through my book about statistics, I came across the topic of linear regression. During the chapter the author begins with explaining that you want to minimize the residuals in order to make your y = a + bx as good a fit as possible: I do understand this, but halfway the chapter all of a sudden the residuals change into sum squares of residuals. Why is this done? I have been googling, but couldn't find the right answer. Who would like to help me understand why the sums of squares of the residuals is used instead of just the sums of residuals?  Kind regards, Bas